The Ising model coupled to 2d orders

TL;DR

This paper investigates the coupling of the Ising model to 2d causal set theory, revealing a complex phase diagram with five phases and a new phase transition driven by matter-causal set interactions.

Contribution

It introduces the first study of matter coupling to causal set theory using the Ising model on 2d orders, uncovering novel phase transitions and structures.

Findings

Five distinct phases identified in the coupled system.

Matter influences the causal set to transition into crystalline phases.

A new phase transition where Ising spins induce crystallinity.

Abstract

In this article we make first steps in coupling matter to causal set theory in the path integral. We explore the case of the Ising model coupled to the 2d discrete Einstein Hilbert action, restricted to the 2d orders. We probe the phase diagram in terms of the Wick rotation parameter \b{eta} and the Ising coupling j and find that the matter and the causal sets together give rise to an interesting phase structure. The couplings give rise to five different phases. The causal sets take on random or crystalline characteristics as described in [1] and the Ising model can be correlated or uncorrelated on the random ordes and correlated, uncorrelated or anti-correlated on the crystalline orders. We find that at least one new phase transition arises, in which the Ising spins push the causal set into the crystalline phase.