aqora

二維“十字”正方形晶格伊辛模型的重正化群解

章國順

Take ”cross” square lattices as Kadanoff, and deal with correlations near critical points, the basic sources on the development of the real-space renormalization group.

Nov 20, 20050 citations

A real-space renormalization-group calculation for the quantum Z 2 gauge theory on a square lattice

Steve T Paik

Abstract We revisit Fradkin and Raby’s real-space renormalization-group method to study the quantum Z 2 gauge theory defined on links forming a two-dimensional square lattice. Following an old suggestion of theirs, a systematic perturbation expansion developed by Hirsch and Mazenko is used to improve the algorithm to second order in an intercell coupling, thereby incorporating the effects of discarded higher energy states. A careful derivation of gauge-invariant effective operators is presented in the Hamiltonian formalism. Renormalization group equations are analyzed near the nontrivial fixed point, reaffirming old work by Hirsch on the dual transverse field Ising model. In addition to recovering Hirsch’s previous findings, critical exponents for the scaling of the spatial correlation length and energy gap in the electric free (deconfined) phase are compared. Unfortunately, their agreement is poor. The leading singular behavior of the ground state energy density is examined near the critical point: we compute both a critical exponent and estimate a critical amplitude ratio.Abstract We revisit Fradkin and Raby’s real-space renormalization-group method to study the quantum Z 2 gauge theory defined on links forming a two-dimensional square lattice. Following an old suggestion of theirs, a systematic perturbation expansion developed by Hirsch and Mazenko is used to improve the algorithm to second order in an intercell coupling, thereby incorporating the effects of discarded higher energy states. A careful derivation of gauge-invariant effective operators is presented in the Hamiltonian formalism. Renormalization group equations are analyzed near the nontrivial fixed point, reaffirming old work by Hirsch on the dual transverse field Ising model. In addition to recovering Hirsch’s previous findings, critical exponents for the scaling of the spatial correlation length and energy gap in the electric free (deconfined) phase are compared. Unfortunately, their agreement is poor. The leading singular behavior of the ground state energy density is examined near the critical point: we compute both a critical exponent and estimate a critical amplitude ratio.

arXiv:2009.06983Journal of Statistical Mechanics Theory and ExperimentJan 1, 20210 citations

The XY model and Kadanoff's variational real space renormalization group

Guðmar Þorleifsson, P.H. Damgaard

Physica A Statistical Mechanics and its ApplicationsOct 1, 19910 citations

Propriedades críticas do modelo z(4) em sistemas bi e tridimensionais

Ezequiel Silva de Souza

A real space renormalization group method is used to investigate the criticality (phase diagrams, critical expoentes and universality classes) of Z(4) model in two and three dimensions. The values of the interaction parameters are chosen in such a way as to cover the complete phase diagrams of the model, which presents the following phases: (i) Paramagnetic (P); (ii) Ferromagnetic (F); (iii) Antiferromagnetic (AF); (iv) Intermediate Ferromagnetic (IF) and Intermediate Antiferromagnetic (IAF). In the hierarquical lattices, generated by renormalization the phase diagrams are exact. It is also possible to obtain approximated results for square and simple cubic lattices. In the bidimensional case a self-dual lattice is used and the resulting phase diagram reproduces all the exact results known for the square lattice. The Migdal-Kadanoff transformation is applied to the three dimensional case and the additional phases previously suggested by Ditzian et al, are not foundA real space renormalization group method is used to investigate the criticality (phase diagrams, critical expoentes and universality classes) of Z(4) model in two and three dimensions. The values of the interaction parameters are chosen in such a way as to cover the complete phase diagrams of the model, which presents the following phases: (i) Paramagnetic (P); (ii) Ferromagnetic (F); (iii) Antiferromagnetic (AF); (iv) Intermediate Ferromagnetic (IF) and Intermediate Antiferromagnetic (IAF). In the hierarquical lattices, generated by renormalization the phase diagrams are exact. It is also possible to obtain approximated results for square and simple cubic lattices. In the bidimensional case a self-dual lattice is used and the resulting phase diagram reproduces all the exact results known for the square lattice. The Migdal-Kadanoff transformation is applied to the three dimensional case and the additional phases previously suggested by Ditzian et al, are not found

Aug 19, 19880 citations

Introduction to real-space renormalization-group methods in critical and chaotic phenomena

Bambi Hu

Physics ReportsNov 1, 1982114 citations

An introduction to the fundamentals of the renormalization group in critical phenomena

Michael N. Barber

Physics ReportsJan 1, 197736 citations

Explanations on the Renormalization of the Dual-dimensional Square Lattices YX Model

Abstract

Related papers

Explanations on the Renormalization of the Dual-dimensional Square Lattices YX Model

Abstract

Related papers