Identification of the critical temperature from non-equilibrium time-dependent quantities

TL;DR

This paper introduces a novel, fast method to identify the critical temperature in spin systems using non-equilibrium, time-dependent measurements without requiring equilibration, applicable to various models including spin glasses.

Contribution

The paper presents a new procedure based on a dimensionless quantity that remains constant at the critical temperature, enabling quick identification without equilibrium.

Findings

The method accurately detects the critical temperature in the ferromagnetic Ising model.

It confirms a finite critical temperature in the one-dimensional Ising spin glass with power-law interactions.

The approach works even in the presence of an external magnetic field.

Abstract

We present a new procedure able to identify and measure the critical temperature. This method is based on the divergence of the relaxation time approaching the critical point in quenches from infinite temperature. We introduce a dimensionless quantity that turns out to be time-independent at the critical temperature. The procedure does not need equilibration and allows for a relatively fast identification of the critical temperature. The method is first tested in the ferromagnetic Ising model and then applied to the one-dimensional Ising spin glass with power-law interactions. Here we always find a finite critical temperature also in presence of a uniform external field, in agreement with the mean-field picture for the low temperature phase of spin glasses.