# Ising chains with competing interactions in presence of long-range couplings

## TL;DR

This paper investigates the complex phase behavior of an Ising spin chain with both short-range competing interactions and long-range ferromagnetic couplings, revealing a rich phase diagram with multiple transition types.

## Contribution

It introduces a comprehensive analysis of the combined effects of short-range frustration and long-range interactions on the phase diagram of Ising chains, extending previous studies by exploring new parameter regions.

## Key findings

- Eight distinct parameter regions with unique phase transition properties
- Presence of both first- and second-order phase transitions
- Identification of multiple critical points

## Abstract

In this paper we study an Ising spin chain with short-range competing interactions in presence of long-range ferromagnetic interactions in the canonical ensemble. The simultaneous presence of the frustration induced by the short-range couplings together with their competition with the long-range term gives rise to a rich thermodynamic phase diagram. We compare our results with the limit in which one of two local interactions is turned off, which was previously studied in the literature. Eight regions of parameters with qualitatively distinct properties are featured, with different first- and second-order phase transition lines and critical points.