Universal behavior of crossover scaling functions for continuous phase transitions

TL;DR

This paper investigates the universal behavior of crossover scaling functions in continuous phase transitions, demonstrating that these functions are consistent across different models within the same universality class and describing the transition from mean-field to non-mean-field behavior.

Contribution

The study provides evidence that crossover scaling functions are universal across models in the same universality class, using phenomenological scaling to describe the entire crossover region.

Findings

Crossover functions are universal across different models.

Scaling describes the transition from mean-field to non-mean-field behavior.

Phenomenological scaling effectively captures the full crossover region.

Abstract

We consider two different systems exhibiting a continuous phase transition into an absorbing state. Both models belong to the same universality class, i.e., they are characterized by the same scaling functions and the same critical exponents. Varying the range of interactions we examine the crossover from the mean-field-like to the non-mean-field scaling behavior. A phenomenological scaling form is applied in order to describe the full crossover region which spans several decades. Our results strongly supports the hypotheses that the crossover function is universal.