On the Simple Approach to Critical Phenomena Description

TL;DR

This paper presents a straightforward real-space field-theoretical method for describing critical phenomena, capturing both critical behavior and crossover to Landau theory within a scalar $^4$ model, differing from Wilson and Parisi approaches.

Contribution

It introduces a simple real 3D approach treating temperature deviations as explicit perturbations, enabling unified description of critical and crossover regimes.

Findings

Successfully describes critical and crossover regions

Uses a different subtraction scheme from Parisi

Applicable within one-loop scalar $^4$ model

Abstract

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 $\phi^4$ model in one-loop approximation.