Spin Resistivity in the Frustrated $J_1-J_2$ Model

TL;DR

This paper investigates how frustration in a $J_1-J_2$ Ising lattice affects the resistivity of itinerant spins, revealing a discontinuity at the first-order transition via Monte Carlo simulations.

Contribution

It introduces a model combining frustrated lattice interactions with itinerant spins and demonstrates the impact of a first-order transition on resistivity.

Findings

Resistivity exhibits a discontinuity at the first-order transition.

Frustration range induces a strong first-order transition.

Monte Carlo simulations effectively capture resistivity behavior.

Abstract

We study in this paper the resistivity encountered by Ising itinerant spins traveling in the so-called $J_1-J_2$ frustrated simple cubic Ising lattice. For the lattice, we take into account the interactions between nearest-neighbors and next-nearest-neighbors, $J_1$ and $J_2$ respectively. Itinerant spins interact with lattice spins via a distance-dependent interaction. We also take into account an interaction between itinerant spins. The lattice is frustrated in a range of $J_2$ in which we show that it undergoes a very strong first-order transition. Using Monte Carlo simulation, we calculate the resistivity $\rho$ of the itinerant spins and show that the first-order transition of the lattice causes a discontinuity of $\rho$.