Effective spin-glass Hamiltonian for the anomalous dynamics of the HMF model

TL;DR

This paper introduces an effective spin-glass Hamiltonian to model the glassy dynamics in the Hamiltonian Mean Field (HMF) model, providing a theoretical framework that aligns with microcanonical simulation results.

Contribution

It presents a novel spin-glass Hamiltonian and derives a self-consistent equation for the glassy order parameter specific to the HMF model.

Findings

The effective Hamiltonian reproduces polarization behavior below the phase transition.

The replica formalism yields a self-consistent equation matching simulation data.

The approach offers insights into the metastable states of the HMF model.

Abstract

We discuss an effective spin-glass Hamiltonian which can be used to study the glassy-like dynamics observed in the metastable states of the Hamiltonian Mean Field (HMF) model. By means of the Replica formalism, we were able to find a self-consistent equation for the glassy order parameter which reproduces, in a restricted energy region below the phase transition, the microcanonical simulations for the polarization order parameter recently introducted in the HMF model.