The XY model with vision cone: non-reciprocal vs. reciprocal interactions

TL;DR

This study investigates how vision cone-based interactions in the XY model influence phase behavior, revealing that non-reciprocal interactions are not necessary for long-range order and uncovering an unexpected order-by-disorder transition.

Contribution

It introduces a novel XY model with vision cone interactions, compares reciprocal and non-reciprocal cases, and provides a theoretical explanation for observed phase behaviors.

Findings

Long-range order occurs at low temperatures regardless of reciprocity.

Non-reciprocal interactions are not essential for long-range order.

An unexpected order-by-disorder transition is identified.

Abstract

We study the behavior of the classical XY model on a two-dimensional square lattice, with interactions occurring within a vision cone of each spin. Via Monte Carlo simulations, we explore one non-reciprocal and two reciprocal implementations of these interactions. The corresponding energy involves couplings that depend non-trivially on the system's configuration, leading to both long-range and quasi-long-range ordered phases at low temperatures. Our results demonstrate that non-reciprocity is not essential for achieving long-range order at low temperatures. Using symmetry arguments, we provide a theoretical framework to explain these findings, and additionally we uncover an unexpected order-by-disorder transition.