Modulated phases in magnetic models frustrated by long-range interactions

TL;DR

This paper investigates a one-dimensional Ising model with competing short-range ferromagnetic and long-range antiferromagnetic interactions, revealing a complex phase diagram with continuously varying domain sizes influenced by an external magnetic field.

Contribution

It introduces a detailed analysis of the zero-temperature phase diagram for a 1D Ising model with long-range interactions, highlighting the effects of long-range forces on domain structures.

Findings

Sequence of up and down domains varies with magnetic field

Domain sizes change continuously between critical fields

Long-range interactions significantly affect phase behavior

Abstract

We study an Ising model in one dimension with short range ferromagnetic and long range (power law) antiferromagnetic interactions. We show that the zero temperature phase diagram in a (longitudinal) field H involves a sequence of up and down domains whose size varies continuously with H, between -H_c and H_c which represent the edge of the ferromagnetic up and down phases. The implications of long range interaction in many body systems are discussed.