Griffiths singularity in quasi-one dimensional restricted $\pm J$ Ising spin glass

TL;DR

This paper analytically and numerically investigates Griffiths singularity in a quasi-one dimensional restricted $ ext{±}J$ Ising spin glass under a magnetic field, revealing essential singularities in thermodynamic quantities.

Contribution

It provides an exact analytical derivation of Griffiths singularity in the model and confirms results through numerical methods, advancing understanding of disordered magnetic systems.

Findings

Explicit form of Griffiths singularity derived

Magnetization approaches a nonzero value at zero field

Analytical results confirmed by numerical simulations

Abstract

We obtain the exact ground state energy of the quasi-one dimensional restricted $\pm J$ Ising spin glass in a uniform magnetic field using the transfer matrix method. Magnetic field dependence allows us to derive the magnetization as a function of concentration and magnetic field. It turns out that, in the limit of zero field, the magnetization tends to a nonzero value with a singular dependence on the magnetic field. We derive the explicit form of the singularity in thermodynamic quantities such as energy $E\simeq E_0+m_0 h + E_1e^{-h_0/h}$, which is an essential singularity known as Griffiths singularity. We confirm our analytical results using the numerical approach based on iterative equations for energy.