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Critical-Phenomena Perturbations, Bounds, and a Field-Theoretical Approach.

George V. Waldo

Published Jan 1, 1972• 0 citations
OpenAlex

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EXACT RENORMALIZATION GROUP EQUATIONS AND THE FIELD THEORETICAL APPROACH TO CRITICAL PHENOMENA

C. Bagnuls, Claude Bervillier

After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as the continuum limit and the renormalizability and the pressure of singularities in the perturbative series are discussed.

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On the Simple Approach to Critical Phenomena Description

Alexander S. Yurkov

Simple field-theoretical approach to critical phenomena is described. In contrast to the Wilson's theory, a description in real 3-dimensions space is used. At the same time the described approach is not the same as Parisi's. Used subtraction scheme is different from the one used by Parisi, but the main point is that we treat changes of $T-T_C$ as explicit perturbations. By such an approach not only the critical domain but also the crossover from critical domain to domain of Landau theory can be described very simply. Consideration is restricted to scalar $ϕ^4$ model in one-loop approximation.

arXiv:1301.1520•Jan 8, 2013•0 citations
Simple field-theoretical approach to critical phenomena is described. In contrast to the Wilson's theory, a description in real 3-dimensions space is used. At the same time the described approach is not the same as Parisi's. Used subtraction scheme is different from the one used by Parisi, but the main point is that we treat changes of T−TCT-T_CT−TC​ as explicit perturbations. By such an approach not only the critical domain but also the crossover from critical domain to domain of Landau theory can be described very simply. Consideration is restricted to scalar ϕ4ϕ^4ϕ4 model in one-loop approximation.