The Experts below are selected from a list of 192 Experts worldwide ranked by ideXlab platform
Nicolás Wschebor - One of the best experts on this subject based on the ideXlab platform.
-
Conformal Invariance and Vector Operators in the O(N) Model
Journal of Statistical Physics, 2019Co-Authors: Gonzalo Polsi, Matthieu Tissier, Nicolás WscheborAbstract:It is widely expected that, for a large class of models, scale invariance implies conformal invariance. A sufficient condition for this to happen is that there exists no integrated Vector Operator, invariant under all internal symmetries of the model, with scaling dimension $$-1$$ - 1 . In this article, we compute the scaling dimensions of Vector Operators with lowest dimensions in the O ( N ) model. We use three different approximation schemes: $$\epsilon $$ ϵ expansion, large N limit and third order of the derivative expansion of Non-Perturbative Renormalization Group equations. We find that the scaling dimensions of all considered integrated Vector Operators are always much larger than $$-1$$ - 1 . This strongly supports the existence of conformal invariance in this model. For the Ising model, an argument based on correlation functions inequalities was derived, which yields a lower bound for the scaling dimension of the Vector perturbations. We generalize this proof to the case of the O ( N ) model with $$N\in \left\{ 2,3,4 \right\} $$ N ∈ 2 , 3 , 4 .
-
Conformal invariance and Vector Operators in the $O(N)$ model
J.Statist.Phys., 2019Co-Authors: Gonzalo Polsi, Matthieu Tissier, Nicolás WscheborAbstract:It is widely expected that, for a large class of models, scale invariance implies conformal invariance. A sufficient condition for this to happen is that there exists no integrated Vector Operator, invariant under all internal symmetries of the model, with scaling dimension $-1$. In this article, we compute the scaling dimensions of Vector Operators with lowest dimensions in the $O(N)$ model. We use three different approximation schemes: $\epsilon$ expansion, large $N$ limit and third order of the Derivative Expansion of Non-Perturbative Renormalization Group equations. We find that the scaling dimensions of all considered integrated Vector Operators are always much larger than $-1$. This strongly supports the existence of conformal invariance in this model. For the Ising model, an argument based on correlation functions inequalities was derived, which yields a lower bound for the scaling dimension of the Vector perturbations. We generalize this proof to the case of the $O(N)$ model with $N\in \left\lbrace 2,3,4 \right\rbrace$.
-
Comment on "A structural test for the conformal invariance of the critical 3d Ising model" by S. Meneses, S. Rychkov, J. M. Viana Parente Lopes and P. Yvernay. arXiv:1802.02319
2018Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:In a recent preprint [ArXiv 1802.02319], Meneses et al. challenge our proof that scale invariance implies conformal invariance for the three-dimensional Ising model [B. Delamotte, M. Tissier and N. Wschebor, Phys. Rev. E 93 (2016), 012144.]. We refute their arguments. We also point out a mistake in their one-loop calculation of the dimension of the Vector Operator $V_\mu$ of lowest dimension which is not a total derivative.
-
Scale invariance implies conformal invariance for the three-dimensional Ising model
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2016Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:Using Wilson renormalization group, we show that if no integrated Vector Operator of scaling dimension −1 exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that scale invariance implies conformal invariance for the three-dimensional Ising model.
-
scale invariance implies conformal invariance for the three dimensional ising model
Physical Review E, 2016Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:Using the Wilson renormalization group, we show that if no integrated Vector Operator of scaling dimension -1 exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that scale invariance implies conformal invariance for the three-dimensional Ising model.
Bertrand Delamotte - One of the best experts on this subject based on the ideXlab platform.
-
Comment on "A structural test for the conformal invariance of the critical 3d Ising model" by S. Meneses, S. Rychkov, J. M. Viana Parente Lopes and P. Yvernay. arXiv:1802.02319
2018Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:In a recent preprint [ArXiv 1802.02319], Meneses et al. challenge our proof that scale invariance implies conformal invariance for the three-dimensional Ising model [B. Delamotte, M. Tissier and N. Wschebor, Phys. Rev. E 93 (2016), 012144.]. We refute their arguments. We also point out a mistake in their one-loop calculation of the dimension of the Vector Operator $V_\mu$ of lowest dimension which is not a total derivative.
-
Scale invariance implies conformal invariance for the three-dimensional Ising model
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2016Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:Using Wilson renormalization group, we show that if no integrated Vector Operator of scaling dimension −1 exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that scale invariance implies conformal invariance for the three-dimensional Ising model.
-
scale invariance implies conformal invariance for the three dimensional ising model
Physical Review E, 2016Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:Using the Wilson renormalization group, we show that if no integrated Vector Operator of scaling dimension -1 exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that scale invariance implies conformal invariance for the three-dimensional Ising model.
Matthieu Tissier - One of the best experts on this subject based on the ideXlab platform.
-
Conformal Invariance and Vector Operators in the O(N) Model
Journal of Statistical Physics, 2019Co-Authors: Gonzalo Polsi, Matthieu Tissier, Nicolás WscheborAbstract:It is widely expected that, for a large class of models, scale invariance implies conformal invariance. A sufficient condition for this to happen is that there exists no integrated Vector Operator, invariant under all internal symmetries of the model, with scaling dimension $$-1$$ - 1 . In this article, we compute the scaling dimensions of Vector Operators with lowest dimensions in the O ( N ) model. We use three different approximation schemes: $$\epsilon $$ ϵ expansion, large N limit and third order of the derivative expansion of Non-Perturbative Renormalization Group equations. We find that the scaling dimensions of all considered integrated Vector Operators are always much larger than $$-1$$ - 1 . This strongly supports the existence of conformal invariance in this model. For the Ising model, an argument based on correlation functions inequalities was derived, which yields a lower bound for the scaling dimension of the Vector perturbations. We generalize this proof to the case of the O ( N ) model with $$N\in \left\{ 2,3,4 \right\} $$ N ∈ 2 , 3 , 4 .
-
Conformal invariance and Vector Operators in the $O(N)$ model
J.Statist.Phys., 2019Co-Authors: Gonzalo Polsi, Matthieu Tissier, Nicolás WscheborAbstract:It is widely expected that, for a large class of models, scale invariance implies conformal invariance. A sufficient condition for this to happen is that there exists no integrated Vector Operator, invariant under all internal symmetries of the model, with scaling dimension $-1$. In this article, we compute the scaling dimensions of Vector Operators with lowest dimensions in the $O(N)$ model. We use three different approximation schemes: $\epsilon$ expansion, large $N$ limit and third order of the Derivative Expansion of Non-Perturbative Renormalization Group equations. We find that the scaling dimensions of all considered integrated Vector Operators are always much larger than $-1$. This strongly supports the existence of conformal invariance in this model. For the Ising model, an argument based on correlation functions inequalities was derived, which yields a lower bound for the scaling dimension of the Vector perturbations. We generalize this proof to the case of the $O(N)$ model with $N\in \left\lbrace 2,3,4 \right\rbrace$.
-
Comment on "A structural test for the conformal invariance of the critical 3d Ising model" by S. Meneses, S. Rychkov, J. M. Viana Parente Lopes and P. Yvernay. arXiv:1802.02319
2018Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:In a recent preprint [ArXiv 1802.02319], Meneses et al. challenge our proof that scale invariance implies conformal invariance for the three-dimensional Ising model [B. Delamotte, M. Tissier and N. Wschebor, Phys. Rev. E 93 (2016), 012144.]. We refute their arguments. We also point out a mistake in their one-loop calculation of the dimension of the Vector Operator $V_\mu$ of lowest dimension which is not a total derivative.
-
Scale invariance implies conformal invariance for the three-dimensional Ising model
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2016Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:Using Wilson renormalization group, we show that if no integrated Vector Operator of scaling dimension −1 exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that scale invariance implies conformal invariance for the three-dimensional Ising model.
-
scale invariance implies conformal invariance for the three dimensional ising model
Physical Review E, 2016Co-Authors: Bertrand Delamotte, Matthieu Tissier, Nicolás WscheborAbstract:Using the Wilson renormalization group, we show that if no integrated Vector Operator of scaling dimension -1 exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that scale invariance implies conformal invariance for the three-dimensional Ising model.
John D. Hey - One of the best experts on this subject based on the ideXlab platform.
-
On the Runge–Lenz–Pauli Vector Operator as an aid to the calculation of atomic processes in laboratory and astrophysical plasmas
Journal of Physics B: Atomic Molecular and Optical Physics, 2015Co-Authors: John D. HeyAbstract:On the basis of the original definition and analysis of the Vector Operator by Pauli (1926 Z. Phys. 36 336–63), and further developments by Flamand (1966 J. Math. Phys. 7 1924–31), and by Becker and Bleuler (1976 Z. Naturforsch. 31a 517–23), we consider the action of the Operator on both spherical polar and parabolic basis state wave functions, both with and without direct use of Pauli’s identity (Valent 2003 Am. J. Phys. 71 171–75). Comparison of the results, with the aid of two earlier papers (Hey 2006 J. Phys. B: At. Mol. Opt. Phys. 39 2641–64, Hey 2007 J. Phys. B: At. Mol. Opt. Phys. 40 4077–96), yields a convenient ladder technique in the form of a recurrence relation for calculating the transformation coefficients between the two sets of basis states, without explicit use of generalized hypergeometric functions. This result is therefore very useful for application to Stark effect and impact broadening calculations applied to high-n radio recombination lines from tenuous space plasmas. We also demonstrate the versatility of the Runge–Lenz–Pauli Vector Operator as a means of obtaining recurrence relations between expectation values of successive powers of quantum mechanical Operators, by using it to provide, as an example, a derivation of the Kramers–Pasternack relation. It is suggested that this Operator, whose potential use in Stark- and Zeeman-effect calculations for magnetically confined fusion edge plasmas (Rosato, Marandet and Stamm 2014 J. Phys. B: At. Mol. Opt. Phys. 47 105702) and tenuous space plasmas ( H II regions) has not been fully explored and exploited, may yet be found to yield a number of valuable results for applications to plasma diagnostic techniques based upon rate calculations of atomic processes.
-
on the runge lenz pauli Vector Operator as an aid to the calculation of atomic processes in laboratory and astrophysical plasmas
Journal of Physics B, 2015Co-Authors: John D. HeyAbstract:On the basis of the original definition and analysis of the Vector Operator by Pauli (1926 Z. Phys. 36 336–63), and further developments by Flamand (1966 J. Math. Phys. 7 1924–31), and by Becker and Bleuler (1976 Z. Naturforsch. 31a 517–23), we consider the action of the Operator on both spherical polar and parabolic basis state wave functions, both with and without direct use of Pauli’s identity (Valent 2003 Am. J. Phys. 71 171–75). Comparison of the results, with the aid of two earlier papers (Hey 2006 J. Phys. B: At. Mol. Opt. Phys. 39 2641–64, Hey 2007 J. Phys. B: At. Mol. Opt. Phys. 40 4077–96), yields a convenient ladder technique in the form of a recurrence relation for calculating the transformation coefficients between the two sets of basis states, without explicit use of generalized hypergeometric functions. This result is therefore very useful for application to Stark effect and impact broadening calculations applied to high-n radio recombination lines from tenuous space plasmas. We also demonstrate the versatility of the Runge–Lenz–Pauli Vector Operator as a means of obtaining recurrence relations between expectation values of successive powers of quantum mechanical Operators, by using it to provide, as an example, a derivation of the Kramers–Pasternack relation. It is suggested that this Operator, whose potential use in Stark- and Zeeman-effect calculations for magnetically confined fusion edge plasmas (Rosato, Marandet and Stamm 2014 J. Phys. B: At. Mol. Opt. Phys. 47 105702) and tenuous space plasmas ( H II regions) has not been fully explored and exploited, may yet be found to yield a number of valuable results for applications to plasma diagnostic techniques based upon rate calculations of atomic processes.
João Penedones - One of the best experts on this subject based on the ideXlab platform.
-
A structural test for the conformal invariance of the critical 3d Ising model
JHEP, 2019Co-Authors: Simão Meneses, João Penedones, Slava Rychkov, J.m. Viana Parente Lopes, Pierre YvernayAbstract:How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current — a non-conserved Vector Operator of dimension exactly (d − 1), whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound Δ$_{V}$ > 5.0 on the scaling dimension of the lowest virial current candidate V, well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model.
-
recursion relations for conformal blocks
Journal of High Energy Physics, 2016Co-Authors: João Penedones, Emilio Trevisani, Masahito YamazakiAbstract:In the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension Δ of the exchanged Operator. In particular, we argue, using representation theory of parabolic Verma modules, that in odd spacetime dimension the singularities are only simple poles. We discuss how to use this information to write recursion relations that determine the conformal blocks. We first recover the recursion relation introduced in [1] for conformal blocks of external scalar Operators. We then generalize this recursion relation for the conformal blocks associated to the four point function of three scalar and one Vector Operator. Finally we specialize to the case in which the Vector Operator is a conserved current.
-
recursion relations for conformal blocks
arXiv: High Energy Physics - Theory, 2015Co-Authors: João Penedones, Emilio Trevisani, Masahito YamazakiAbstract:In the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension $\Delta$ of the exchanged Operator. In particular, we argue, using representation theory of parabolic Verma modules, that in odd spacetime dimension the singularities are only simple poles. We discuss how to use this information to write recursion relations that determine the conformal blocks. We first recover the recursion relation introduced in 1307.6856 for conformal blocks of external scalar Operators. We then generalize this recursion relation for the conformal blocks associated to the four point function of three scalar and one Vector Operator. Finally we specialize to the case in which the Vector Operator is a conserved current.
