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E M Terentjev - One of the best experts on this subject based on the ideXlab platform.
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sound attenuation derived from Quenched Disorder in solids
arXiv: Disordered Systems and Neural Networks, 2021Co-Authors: Bingyu Cui, Alessio Zaccone, E M TerentjevAbstract:In scattering experiments, the dynamical structure factor (DSF) characterizes inter-particle correlations and their time evolution. We analytically evaluated the DSF of Disordered solids with Disorder in the spring constant, by averaging over Quenched Disorder in the values of lattice bond strength, along the acoustic branch. The width of the resulting acoustic excitation peak is treated as the effective damping constant $\Gamma(q)$, which we found to grow linearly with exchanged momentum $q$. This is verified by numerically calculating a model system consisting of harmonic linear chains with Disorder in spring constant. We also found that the Quenched averaging of the vibrational density of states produces a characteristic peak at a frequency related to the average acoustic resonance. Such a peak (the excess over Debye law) may be related to the "boson peak" frequently discussed in Disordered solids, in our case explicitly arising from the Quenched Disorder in the distribution of spring constants.
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microtubule buckling in an elastic matrix with Quenched Disorder
Journal of Chemical Physics, 2018Co-Authors: Chengtai Lee, E M TerentjevAbstract:The intracellular elastic matrix has been recognized as an important factor to stabilize microtubules and increase their critical buckling force Pc in vivo. This phenomenon was qualitatively explained by the Winkler model, which investigated the buckling of a filament embedded in a homogeneous elastic medium. However, the assumption of homogeneity of the matrix in Winkler’s, and other advanced models, is unrealistic inside cells, where the local environment is highly variable along the filament. Considering this to be a Quenched-Disorder system, we use a Poisson distribution for confinements and apply the replica technique combined with the Gaussian variational method to study the buckling of a long filament. The results show two types of filament bucklings: one corresponding to the first-order, and the other to a continuous second-order phase transition. The critical point, i.e., the switch from first- to second-order buckling transition, is induced by the increase in Disorder strength. We also discover that this random Disorder of the elastic environment destabilizes the filament by decreasing Pc from the Winkler result and the matrix with stronger mean elasticity has a stronger role of Disorder (inhomogeneity). For microtubules in vivo, buckling follows the discontinuous first-order transition, with Pc reduced to the fraction between 0.9 and 0.75 of the Winkler prediction for the homogeneous elastic matrix. We also show that Disorder can affect the force-displacement relationship at non-zero temperature, while at zero temperature this effect vanishes.The intracellular elastic matrix has been recognized as an important factor to stabilize microtubules and increase their critical buckling force Pc in vivo. This phenomenon was qualitatively explained by the Winkler model, which investigated the buckling of a filament embedded in a homogeneous elastic medium. However, the assumption of homogeneity of the matrix in Winkler’s, and other advanced models, is unrealistic inside cells, where the local environment is highly variable along the filament. Considering this to be a Quenched-Disorder system, we use a Poisson distribution for confinements and apply the replica technique combined with the Gaussian variational method to study the buckling of a long filament. The results show two types of filament bucklings: one corresponding to the first-order, and the other to a continuous second-order phase transition. The critical point, i.e., the switch from first- to second-order buckling transition, is induced by the increase in Disorder strength. We also discover ...
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stretching semiflexible filaments with Quenched Disorder
Bulletin of the American Physical Society, 2011Co-Authors: Panayotis Benetatos, E M TerentjevAbstract:fects in the Kratky-Porod chain with a random sequence of stiffness constants. In a recent paper [16], we studied the response of a weakly bending WLC with arc-length dependent spontaneous curvature to a stretching force applied at its ends. We specifically considered the case of sinusoidally varying spontaneous curvature which allows us to treat the general case via Fourier transformation. This simple and analytically tractable model appears to be particularly well suited for the study of Quenched Disorder in the spontaneous curvature of a filament under tension. This is the subject of the present paper. A similar calculation with a different method (which is in principle valid) was attempted in Ref. [17], but a mistake in the way the thermodynamic limit was taken led to the incorrect conclusion that sequence Disorder has no effect on elasticity. Here, we use the replica trick to calculate the effect of uncorrelated Quenched Disorder and we obtain the forceextension relationsip as well as force-transverse-width relationship. We compare our results with those obtained in the context of annealed Disorder. Although, as we show, the two cases (Quenched and annealed) are indistinguishable in the limit of weak Disorder, our results for
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nematic isotropic transition with Quenched Disorder
Physical Review E, 2006Co-Authors: Loukas Petridis, E M TerentjevAbstract:Nematic elastomers do not show the discontinuous, first-order, phase transition that the Landau-De Gennes mean field theory predicts for a quadrupolar ordering in three dimensions. We attribute this behavior to the presence of network crosslinks, which act as sources of Quenched orientational Disorder. We show that the addition of weak random anisotropy results in a singular renormalization of the Landau-De Gennes expression, adding an energy term proportional to the inverse quartic power of order parameter Q. This reduces the first-order discontinuity in Q. For sufficiently high Disorder strength the jump disappears altogether and the phase transition becomes continuous, in some ways resembling the supercritical transitions in external field.
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Quenched Disorder and spin glass correlations in xy nematics
Journal of Physics A, 2006Co-Authors: Loukas Petridis, E M TerentjevAbstract:We present a theoretical study of the equilibrium ordering in a 3D XY nematic system with Quenched random Disorder. Within this model, treated with the replica trick and Gaussian variational method, the correlation length is obtained as a function of the local nematic order parameter Q and the effective Disorder strength ?. These results, and ? ~ (1/?) e??, clarify what happens in the limiting cases of diminishing Q and ?, that is near a phase transition of a pure system. In particular, it is found that Quenched Disorder is irrelevant as Q ? 0 and hence does not change the character of the continuous XY nematic?isotropic phase transition. We discuss how these results compare with experiments and simulations.
A Asamitsu - One of the best experts on this subject based on the ideXlab platform.
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coexistence of long ranged charge and orbital order and spin glass state in single layered manganites with weak Quenched Disorder
EPL, 2007Co-Authors: T Arima, R Mathieu, Y Kaneko, A Asamitsu, Masaki Uchida, Y S LeeAbstract:The relationship between orbital and spin degrees of freedom in the single crystals of the hole-doped Pr1-xCa1+xMnO4, 0.3 ≤x ≤ 0.7 has been investigated by means of ac-magnetometry and charge transport. We show that in an intermediate underdoped region, with 0.35 ≤x < 0.5, the "orbital-master spin-slave" relationship commonly observed in half-doped manganites does not take place. The long-ranged charge-orbital order is not accompanied by an antiferromagnetic transition at low temperatures, but by a frustrated short-ranged magnetic state bringing forth a spin-glass phase. We discuss in detail the nature and origin of this true spin-glass state, which, as in the half-doped manganites with large Quenched Disorder, is not related to the macroscopic phase separation observed in crystals with minor defects or impurities.
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coexistence of long ranged charge and orbital order and spin glass state in single layered manganites with weak Quenched Disorder
arXiv: Materials Science, 2007Co-Authors: T Arima, R Mathieu, Y Kaneko, A Asamitsu, Masaki Uchida, Y S LeeAbstract:The relationship between orbital and spin degrees of freedom in the single-crystals of the hole-doped Pr$_{1-x}$Ca$_{1+x}$MnO$_4$, 0.3 $\leq$ $x$ $\leq$ 0.7, has been investigated by means of ac-magnetometry and charge transport. Even though there is no cation ordering on the $A$-site, the Quenched Disorder is extremely weak in this system due to the very similar ionic size of Pr$^{3+}$ and Ca$^{2+}$. A clear asymmetric response of the system to the under- (respective over-) hole doping was observed. The long-ranged charge-orbital order established for half doping ($x$=0.5) subsists in the over-doping case ($x$ $>$ 0.5), albeit rearranged to accommodate the extra holes introduced in the structure. The charge-orbital order is however destabilized by the presence of extra localized electrons (under-doping, $x$ $<$ 0.5), leading to its disappearance below $x$=0.35. We show that in an intermediate under-doped region, with 0.35 $\leq$ $x$ $<$ 0.5, the ``orbital-master spin-slave'' relationship commonly observed in half-doped manganites does not take place. The long-ranged charge-orbital order is not accompanied by an antiferromagnetic transition at low temperatures, but by a frustrated short-ranged magnetic state bringing forth a spin-glass phase. We discuss in detail the nature and origin of this spin-glass state, which, as in the half-doped manganites with large Quenched Disorder, is not related to the macroscopic phase separation observed in crystals with minor defects or impurities.
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effect of Quenched Disorder on charge orbital spin ordering in single layer manganites
Journal of the Physical Society of Japan, 2006Co-Authors: Masaya Uchida, Yoshinori Tokura, Yoshio Matsui, R Mathieu, Y Kaneko, A Asamitsu, Reiji Kumai, Y TomiokaAbstract:Structural and magnetic properties have been investigated for half-doped single-layer manganites RE 0.5 Sr 1.5 MnO 4 [ RE = La, (La, Pr), Pr, Nd, Sm, and Eu]. Analyses of electron diffraction and ac susceptibility measurements have revealed that the long-range charge–orbital ordering (CO–OO) state as observed in La 0.5 Sr 1.5 MnO 4 is suppressed for the other materials: the CO–OO transition temperature, as well as the correlation length decreases with a decrease in the cation size of RE . Such a short-range CO–OO state shows a spin-glass behavior at low temperatures. A new electronic phase diagram is established with Quenched Disorder as the control parameter.
Subir Sachdev - One of the best experts on this subject based on the ideXlab platform.
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quantum electrodynamics in 2 1 dimensions with Quenched Disorder quantum critical states with interactions and Disorder
Physical Review B, 2017Co-Authors: Alex Thomson, Subir SachdevAbstract:Quantum electrodynamics in 2+1-dimensions (QED$_3$) is a strongly coupled conformal field theory (CFT) of a U(1) gauge field coupled to $2N$ two-component massless fermions. The $N=2$ CFT has been proposed as a ground state of the spin-1/2 kagome Heisenberg antiferromagnet. We study QED$_3$ in the presence of weak Quenched Disorder in its two spatial directions. When the Disorder explicitly breaks the fermion flavor symmetry from SU($2N$)$\rightarrow$U(1)$\times$SU($N$) but preserves time-reversal symmetry, we find that the theory flows to a non-trivial fixed line at non-zero Disorder with a continuously varying dynamical critical exponent $z>1$. We determine the zero-temperature flavor (spin) conductivity along the critical line. Our calculations are performed in the large-$N$ limit, and the Disorder is handled using the replica method.
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from stripe to checkerboard ordering of charge density waves on the square lattice in the presence of Quenched Disorder
Physical Review B, 2006Co-Authors: Adrian Del Maestro, Bernd Rosenow, Subir SachdevAbstract:We discuss the effects of Quenched Disorder on a model of charge density wave (CDW) ordering on the square lattice. Our model may be applicable to the cuprate superconductors, where a random electrostatic potential exists in the $\mathrm{Cu}{\mathrm{O}}_{2}$ planes as a result of the presence of charged dopants. We argue that the presence of a random potential can affect the unidirectionality of the CDW order, characterized by an Ising order parameter. Coupling to a unidirectional CDW, the random potential can lead to the formation of domains with 90\ifmmode^\circ\else\textdegree\fi{} relative orientation, thus tending to restore the rotational symmetry of the underlying lattice. We find that the correlation length of the Ising order can be significantly larger than the CDW correlation length. For a checkerboard CDW on the other hand, Disorder generates spatial anisotropies on short length scales and, thus, some degree of unidirectionality. We quantify these Disorder effects and suggest techniques for analyzing the spatially dependent local density of states data measured in scanning tunneling microscopy experiments.
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from stripe to checkerboard ordering of charge density waves on the square lattice in the presence of Quenched Disorder
Physical Review B, 2006Co-Authors: Adrian Del Maestro, Bernd Rosenow, Subir SachdevAbstract:We discuss the effects of Quenched Disorder on a model of charge density wave (CDW) ordering on the square lattice. Our model may be applicable to the cuprate superconductors, where a random electrostatic potential exists in the CuO2 planes as a result of the presence of charged dopants. We argue that the presence of a random potential can affect the unidirectionality of the CDW order, characterized by an Ising order parameter. Coupling to a unidirectional CDW, the random potential can lead to the formation of domains with 90 degree relative orientation, thus tending to restore the rotational symmetry of the underlying lattice. We find that the correlation length of the Ising order can be significantly larger than the CDW correlation length. For a checkerboard CDW on the other hand, Disorder generates spatial anisotropies on short length scales and thus some degree of unidirectionality. We quantify these Disorder effects and suggest new techniques for analyzing the local density of states (LDOS) data measured in scanning tunneling microscopy experiments.
A B Babaev - One of the best experts on this subject based on the ideXlab platform.
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the critical behavior of the two dimensional three state potts model on a triangular lattice with Quenched Disorder
Materials Letters, 2019Co-Authors: Akai K Murtazaev, A B BabaevAbstract:Abstract The critical behavior of the two-dimensional three-state antiferromagnetic Potts model with Quenched Disorder on a triangular lattice is investigated by the Monte Carlo method. Static critical exponents for the susceptibility γ , the magnetization β , the specific heat α , and the exponent of the correlation radius ν at spin concentrations p = 0.90; 0.80; 0.70; 0.65 are calculated on the basis of the finite-size scaling theory. The critical exponents are found to be increasing with a rise in Disorder without violating the feasibility of scaling equation 2 β ν + γ ν = d , while relations γ/ν and β/ν remain unchanged. This behavior of the critical exponents we have come to associate with the weak universality of a critical behavior typical for Disordered systems.
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critical properties of the three dimensional ising model with Quenched Disorder
Journal of Magnetism and Magnetic Materials, 2009Co-Authors: Akai K Murtazaev, A B BabaevAbstract:Abstract The static critical properties of the three-dimensional Ising model with Quenched Disorder are studied by the Monte-Carlo (MC) method on a simple cubic lattice, in which the Quenched Disorder is distributed as nonmagnetic impurities by the canonical manner. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p =1.0; 0.95; 0.9; 0.8; 0.7; 0.6. The systems of non-linear sizes L × L × L , L =20–60 are researched. On the basis of the finite-size scaling (FSS) theory, the static critical exponents of specific heat α , susceptibility γ , magnetization β , and an exponent of the correlation radius in a studied interval of concentrations p are calculated. It is shown that the three-dimensional Ising model with Quenched Disorder has two regimes of the critical behavior universality in a dependence on nonmagnetic impurities.
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critical behavior of a cubic lattice 3d ising model for systems with Quenched Disorder
Journal of Experimental and Theoretical Physics, 2004Co-Authors: Akai K Murtazaev, I K Kamilov, A B BabaevAbstract:A Monte Carlo method is applied to simulate the static critical behavior of a cubic-lattice 3D Ising model for systems with Quenched Disorder. Numerical results are presented for the spin concentrations of p = 1.0, 0.95, 0.9, 0.8, 0.6 on L × L × L lattices with L = 20–60 under periodic boundary conditions. The critical temperature is determined by the Binder cumulant method. A finite-size scaling technique is used to calculate the static critical exponents α, β, γ, and ν (for specific heat, susceptibility, magnetization, and correlation length, respectively) in the range of p under study. Universality classes of critical behavior are discussed for three-dimensional diluted systems.
Ofer Aharony - One of the best experts on this subject based on the ideXlab platform.
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renormalization group in field theories with quantum Quenched Disorder
Physical Review Letters, 2018Co-Authors: Vladimir Narovlansky, Ofer AharonyAbstract:We study the renormalization group flow in general quantum field theories with Quenched Disorder, focusing on random quantum critical points. We show that in Disorder-averaged correlation functions the flow mixes local and nonlocal operators. This leads to a new critical exponent related to the Disorder (as in classical Disorder). We show that the time coordinate is rescaled at each renormalization group step, leading to anisotropic spacetime scaling at critical points. We write a universal formula for the dynamical scaling exponent z for weak Disorder.
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renormalization group flow in field theories with Quenched Disorder
Physical Review D, 2018Co-Authors: Ofer Aharony, Vladimir NarovlanskyAbstract:In this paper we analyze the renormalization group (RG) flow of field theories with Quenched Disorder, in which the couplings vary randomly in space. We analyze both classical (Euclidean) Disorder and quantum Disorder, emphasizing general properties rather than specific cases. The RG flow of the Disorder-averaged theories takes place in the space of their coupling constants and also in the space of distributions for the Disordered couplings, and the two mix together. We write down a generalization of the Callan-Symanzik equation for the flow of Disorder-averaged correlation functions. We find that local operators can mix with the response of the theory to local changes in the Disorder distribution, and that the generalized Callan-Symanzik equation mixes the Disorder averages of several different correlation functions. For classical Disorder we show that this can lead to new types of anomalous dimensions and to logarithmic behavior at fixed points. For quantum Disorder we find that the RG flow always generates a rescaling of time relative to space, which at a fixed point generically leads to Lifshitz scaling. The dynamical scaling exponent z behaves as an anomalous dimension (as in other non-relativistic RG flows), and we compute it at leading order in perturbation theory in the Disorder for a general theory. Our results agree with a previous perturbative computation by Boyanovsky and Cardy, and with a holographic Disorder computation of Hartnoll and Santos. We also find in quantum Disorder that local operators mix with non-local (in time) operators under the RG, and that there are critical exponents associated with the Disorder distribution that have not previously been discussed. In large N theories the Disorder averages may be computed exactly, and we verify that they are consistent with the generalized Callan-Symanzik equations.
