aqora

Coherent anomalies and critical phenomena in spin systems : systematic cluster-mean-field approximations

眞理香取

Jan 1, 19880 citations

Skeletonization, Fluctuating Mean-Field Approximations and Coherent Anomalies in Critical Phenomena

Masuo Suzuki

Concepts of skeleton order parameters and their conjugate symmetry breaking skeleton fields are introduced in order to describe the phase transition of the relevant system.It is shown that the "skeletonization" of Hamiltonians is very useful in understanding the essence of phase transitions.Singularities of skeleton susceptibilities are studied in general.There are given some examples in spin systems.Fluctuating mean-field approximations are introduced to study phase transitions qualitatively, namely to find more accurate values of critical points even in frustrated spin systems.This idea gives the basis of the coherent anomaly method (CAM).This new method is explained briefly to obtain non-classical critical exponents in cluster mean-field approximations on the basis of the concept of coherent anomalies.§ 1. IntroductionConcepts of skeleton order parameters and their conjugate symmetry breaking skeleton fields are introduced in order to describe the phase transition of the relevant system.It is shown that the "skeletonization" of Hamiltonians is very useful in understanding the essence of phase transitions.Singularities of skeleton susceptibilities are studied in general.There are given some examples in spin systems.Fluctuating mean-field approximations are introduced to study phase transitions qualitatively, namely to find more accurate values of critical points even in frustrated spin systems.This idea gives the basis of the coherent anomaly method (CAM).This new method is explained briefly to obtain non-classical critical exponents in cluster mean-field approximations on the basis of the concept of coherent anomalies.§ 1. Introduction

Progress of Theoretical Physics SupplementJan 1, 198622 citations

Critical Phenomena in Statistical Mechanics — Aspects of Renormalization Group Theory

Michael Ellis Fisher

Springer eBooksJan 1, 19800 citations

Statistical Mechanical Theory of Cooperative Phenomena.I. General Theory of Fluctuations, Coherent Anomalies and Scaling Exponents with Simple Applications to Critical Phenomena

Masuo Suzuki

A general method is proposed to study non-classical scaling behaviors of cooperative systems. This is based on the appearance of a "coherent anomaly" in mean-field-type or classical approximations of cooperative systems. The degree of approximation is analytically continued to construct a parameterized expression of a whole set of approximations, using Kubo's linear response theory. General relations between scaling (or critical) exponents and "coherent-anomaly exponents" are derived using the theory of envelope and are also obtained from a finite-degree-of-approximation scaling, which is inspired by Fisher's finite-size scaling. The present coherent-anomaly method (CAM) is promising for calculating analytically non-classical scaling exponents in cooperative phenomena. A general scheme of CAM in critical phenomena is presented. It is shown that even the combination of the Weiss and Bethe approximations gives rather good estimates of static and dynamic critical exponents.A general method is proposed to study non-classical scaling behaviors of cooperative systems. This is based on the appearance of a "coherent anomaly" in mean-field-type or classical approximations of cooperative systems. The degree of approximation is analytically continued to construct a parameterized expression of a whole set of approximations, using Kubo's linear response theory. General relations between scaling (or critical) exponents and "coherent-anomaly exponents" are derived using the theory of envelope and are also obtained from a finite-degree-of-approximation scaling, which is inspired by Fisher's finite-size scaling. The present coherent-anomaly method (CAM) is promising for calculating analytically non-classical scaling exponents in cooperative phenomena. A general scheme of CAM in critical phenomena is presented. It is shown that even the combination of the Weiss and Bethe approximations gives rather good estimates of static and dynamic critical exponents.

Journal of the Physical Society of JapanDec 15, 1986210 citations

Lee-Yang Theorem on Generalized Ising Models with Degeneracy

M. Yamashita, H. Nakano

Progress of Theoretical Physics Vol. 65 No. 5 (1981) pp. 1603-1612 Distribution of Zeros of the Partition Function in the First and Second Order Phase Transitions Keiji Yamada, Huzio Nakano and Mamoru Yamashita Progress of Theoretical Physics Vol. 67 No. 2 (1982) pp. 375-388 Landau Theory and the Inverse Temperature Series Expansion in the Method of Symmetry Breaking Potential Mamoru Yamashita Progress of Theoretical Physics Supplement No.87 (1986) pp. 1-22 Skeletonization, Fluctuating Mean-Field Approximations and Coherent Anomalies in Critical Phenomena Masuo SuzukiProgress of Theoretical Physics Vol. 65 No. 5 (1981) pp. 1603-1612 Distribution of Zeros of the Partition Function in the First and Second Order Phase Transitions Keiji Yamada, Huzio Nakano and Mamoru Yamashita Progress of Theoretical Physics Vol. 67 No. 2 (1982) pp. 375-388 Landau Theory and the Inverse Temperature Series Expansion in the Method of Symmetry Breaking Potential Mamoru Yamashita Progress of Theoretical Physics Supplement No.87 (1986) pp. 1-22 Skeletonization, Fluctuating Mean-Field Approximations and Coherent Anomalies in Critical Phenomena Masuo Suzuki

Progress of Theoretical PhysicsFeb 1, 19781 citation

INTRODUCTION TO PHASE TRANSITIONS, CRITICAL PHENOMENA AND COHERENT ANOMALY

Masuo Suzuki, Xiao Hu, Naomichi Hatano +4 more

WORLD SCIENTIFIC eBooksSep 1, 19950 citations

Skeletonization, Fluctuating Mean-Field Approximations and Coherent Anomalies in Critical Phenomena (Some Recent Development in the Statistical Mechanics of Magnetism)

Related papers

Skeletonization, Fluctuating Mean-Field Approximations and Coherent Anomalies in Critical Phenomena (Some Recent Development in the Statistical Mechanics of Magnetism)

Related papers