Size dependence of the internal energy in Ising and vector spin glasses

TL;DR

This paper investigates how the internal energy per spin in Ising and vector spin glasses scales with system size and temperature, revealing complex behavior of size correction exponents near critical points.

Contribution

It provides a numerical analysis of size correction exponents in spin glasses, highlighting their non-trivial temperature dependence near criticality.

Findings

The size correction exponent x varies with temperature, showing a minimum near the critical temperature.

x decreases from zero at low temperatures and then increases sharply above the critical temperature.

The behavior of x below and at the critical temperature is more complex than existing models suggest.

Abstract

We study numerically the scaling correction to the internal energy per spin as a function of system size and temperature in a variety of Ising and vector spin glasses. From a standard scaling analysis we estimate the effective size correction exponent x at each temperature. For each system with a finite ordering temperature, as temperature is increased from zero, x initially decreases regularly until it goes through a minimum at a temperature close to the critical temperature, and then increases strongly. The behavior of the exponent x at and below the critical temperature is more complex than suggested by the model for the size correction that relates x to the domain-wall stiffness exponent.