Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions

TL;DR

This paper investigates the interface free-energy exponent in a one-dimensional long-range Ising spin glass model, aiming to understand the transition between broken replica symmetry and droplet behavior, supported by numerical analysis.

Contribution

It provides a calculation of the interface free-energy exponent in a long-range 1D Ising spin glass, exploring its behavior across different regimes and addressing finite-size effects.

Findings

Numerical results are significantly affected by finite-size problems.

The calculated exponent offers insights into the phase transition between different spin-glass states.

Supportive numerical work clarifies assumptions in the theoretical calculations.

Abstract

The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems.