The lower bound of barrier-energy in spin glasses: a calculation of the exponent on hierarchical lattice

TL;DR

This paper establishes a size-independent lower bound for barrier energy in spin glasses and calculates a related exponent on hierarchical lattices, revealing insights into the energy landscape and dynamics of spin systems.

Contribution

It introduces a size-independent lower bound for barrier energy in spin glasses and computes the exponent on hierarchical lattices, linking it to domain wall energy.

Findings

Lower bound to barrier energy is system size independent.

Calculated exponent matches the domain wall energy exponent.

Existence of a dynamical pathway bypassing local maxima.

Abstract

We argue that the lower bound to the barrier energy to flip an up/down spin domain embedded in a down/up spin environment for Ising spin glass is independent of the size of the system. The argument shows the existence of at least one dynamical way through which it is possible to bypass local maxima in the phase space. For an arbitrary case where one flips any cluster of spin of size $l$, we have numerically calculated a lower bound to the exponent $\psi$ characterizing the barrier one has to overcome. In this case $\psi$ corresponding to the lower bound calculated on hierarchical lattice comes out to be equal to $\theta $ the exponent characterizing the domain wall energy in ground state.