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Real-space renormalization-group approaches for two-dimensional Gaussian Ising spin glass

Fernando Dantas Nobre

Physics Letters ADec 1, 199810 citations

Real-space renormalization group investigation of the three-dimensional semi-infinite mixed spin ising model

Noureddine Benayad, J. Zittartz

The European Physical Journal BFeb 1, 199052 citations

Real-space renormalization group investigation of pure and disordered mixed spin Ising models ond-dimensional lattices

Noureddine Benayad

The European Physical Journal BFeb 1, 199047 citations

Real Space Renormalization Group Calculations for Spin Glasses

A. P. Young

Springer eBooksJan 1, 19770 citations

ランダム量子スピン系の実空間くりこみ群による解析

涼二宮崎, Ryoji Miyazaki

The present thesis investigates phase transitions and critical phenomena in the random transverse-field Ising models by means of a real-space renormalization-group method.The analysis is intended to examine the presence of infinite-randomness fixed points in the models in a renormalization-group picture.Infinite-randomness fixed points are concerned with peculiar critical phenomena, which have been established in a study of the one-dimensional random transverse-field Ising model.Subsequent studies have conjectured the presence of the fixed point in some cases.The thesis mainly examines such two cases: the two-and three-dimensional Ising spin glasses in a transverse field and the one-dimensional Ising spin glass with the power-law interaction in a transverse field.The latter is not directly tackled.Instead, we introduce and analyze the hierarchical model which is expected to show similar critical phenomena.A real-space renormalization-group method is exploited in the thesis.We develop the method in a model without randomness first.The method reproduces some previously known results of transition points and critical exponents in pure and disordered cases.The spin-glass models mentioned above are investigated with the method.We find evidence of the presence of infinite-randomness fixed points in these cases as a result, which supports the conjectures.The present thesis investigates phase transitions and critical phenomena in the random transverse-field Ising models by means of a real-space renormalization-group method.The analysis is intended to examine the presence of infinite-randomness fixed points in the models in a renormalization-group picture.Infinite-randomness fixed points are concerned with peculiar critical phenomena, which have been established in a study of the one-dimensional random transverse-field Ising model.Subsequent studies have conjectured the presence of the fixed point in some cases.The thesis mainly examines such two cases: the two-and three-dimensional Ising spin glasses in a transverse field and the one-dimensional Ising spin glass with the power-law interaction in a transverse field.The latter is not directly tackled.Instead, we introduce and analyze the hierarchical model which is expected to show similar critical phenomena.A real-space renormalization-group method is exploited in the thesis.We develop the method in a model without randomness first.The method reproduces some previously known results of transition points and critical exponents in pure and disordered cases.The spin-glass models mentioned above are investigated with the method.We find evidence of the presence of infinite-randomness fixed points in these cases as a result, which supports the conjectures.

Mar 1, 20140 citations

Replica Real Space Renormalization Group for Spin Glasses

J. R. L. de Almeida, S. Coutinho

We construct a real space renormalization group (RG) approach for Ising spin glasses on hypercubic lattices within the scheme of the Migdal-Kadanoff approximation using replicas. Our replica symmetric solution yields results consistent with simple decimation previously obtained and the introduction of breaking of replica symmetry within the RG is discussed, which inserts in a natural fashion non-linear RG into the problem.

arXiv:cond-mat/9312020Dec 5, 19930 citations

Real space renormalization group investigation of three-dimensional Ising spin glasses

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