# Equilibrium structure and off-equilibrium kinetics of a magnet with tunable frustration

## TL;DR

This study investigates how tunable frustration in a 2D random-bond Ising model affects equilibrium structures and off-equilibrium dynamics, revealing diverse slow relaxation behaviors linked to different magnetic phases.

## Contribution

It introduces a numerical analysis of a tunable frustration parameter in the Ising model, highlighting the impact on phase behavior and relaxation dynamics.

## Key findings

- Logarithmically slow kinetics in ferromagnetic and antiferromagnetic phases.
- Algebraic relaxation observed in spin glass phase.
- Frustration level significantly influences dynamical properties.

## Abstract

We study numerically a two-dimensional random-bond Ising model where frustration can be tuned by varying the fraction $a$ of antiferromagnetic coupling constants. At low temperatures the model exhibits a phase with ferromagnetic order for sufficiently small values of $a$, $a<a_f$. In an intermediate range $a_f<a<a_a$ the system is paramagnetic, with spin glass order expected right at zero temperature. For even larger values $a>a_a$ an antiferromagnetic phase exists. After a deep quench from high temperatures, slow evolution is observed for any value of $a$. We show that different amounts of frustration, tuned by $a$, affect the dynamical properties in a highly non trivial way. In particular, the kinetics is logarithmically slow in phases with ferromagnetic or antiferromagnetic order, whereas evolution is faster, i.e. algebraic, when spin glass order is prevailing. An interpretation is given in terms of the different nature of phase space.