Nature of the global fluctuations in the spherical model at criticality

TL;DR

This paper investigates the universal behavior of global fluctuations at criticality in the spherical model, revealing non-Gaussian, dimension-dependent distribution characteristics through exact analysis of magnetization statistics.

Contribution

It provides an exact analysis of the magnetization distribution in the spherical model at criticality, highlighting non-Gaussian and asymmetric features depending on system dimension.

Findings

Distribution is non-Gaussian and asymmetric

Distribution depends on system dimension (2<d<4)

Relation to extreme statistics of wavelength modes

Abstract

We study the universal nature of global fluctuations in the critical regime of the spherical model by evaluating the exact distribution of the magnetization and its absolute value in the thermodynamical limit, in the presence of a conjugate field. We show that the probability distribution function for this model is described by non-Gaussian asymptotics and non-symmetric characteristics which depend on the dimension of the system 2<d<4. Relation with extreme statistics of independent wavelength modes is discussed.