Work

Universal and Nonuniversal Signatures in the Scaling Functions of Critical Variables

Year: 2025

Type: article

Abstract: At criticality, the magnetization M of a d-dimensional Ising system with N spins is distributed such that the probability density function of m=M/N^{y_{H}/d}, with y_{H} universal exponent, converges to a limit f(m). The expectation that f should furnish a hallmark of universal behavior contrasts with its sensible dependence on nonuniversal features. We show that both nonuniversal amplitudes and universal exponents of leading power law singularities in all large deviation functions are determined by the fact that, due to extensivity, f(m)∼_{|m|≫1}exp(-c|m|^{δ+1}), with δ=y_{H}/(d-y_{H}) and c a nonuniversal coefficient. This unexplored scenario implies a universal form of central limit theorem at criticality and is confirmed by exact calculations for mean field Ising models in equilibrium and for anomalous diffusion models, with M replaced by displacement and N by time.

Source: Physical Review Letters

DOI: 10.1103/physrevlett.134.127102

Authors: Gianluca Teza, Attilio L. Stella

Institutions: Max Planck Institute for the Physics of Complex Systems, Weizmann Institute of Science, University of Padua, Istituto Nazionale di Fisica Nucleare

Language: English

Topic: Theoretical and Computational Physics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,750

Funders: National Science Foundation, Simons Foundation, United States - Israel Binational Science Foundation, Weizmann Institute of Science