Phase transitions in 2d orders coupled to the Ising model

Abstract

The $2$d orders are a sub class of causal sets, which is especially amenable to computer simulations. Past work has shown that the $2$d orders have a first order phase transition between a random and a crystalline phase. When coupling the $2$d orders to the Ising model, this phase transition coincides with the transition of the Ising model. The coupled system also shows a new phase, at negative $\beta$, where the Ising model induces the geometric transition. In this article we examine the phase transitions of the coupled system, to determine their order, as well as how they scale when the system size is changed. We find that the transition at positive $\beta$ seems to be of mixed order, while the two transitions at negative $\beta$ appear continous/ first order for the Ising model/ the geometry respectively. The scaling of the observables with the system size on the other hand is fairly simple, and does, where applicable, agree with that found for the pure $2$d orders. We find that the location of these transitions has fractional scaling in the system size.

34 pages, 22 figures, v2 matches journal version, to appear in CQG

References in corpus (14)

• A Classical Sequential Growth Dynamics for Causal Sets
• Thermodynamics and dynamics of systems with long-range interactions
• The Scalar Curvature of a Causal Set
• Causal set d'Alembertians for various dimensions
• Status of the asymptotic safety paradigm for quantum gravity and matter
• Fourth-Order Cumulants to Characterize the Phase Transitions of a Spin-1 Ising Model
• Towards a Definition of Locality in a Manifoldlike Causal Set
• Quantum geometry of 2d gravity coupled to unitary matter
• Evidence for a Phase Transition in 2D Causal Set Quantum Gravity
• A closed form expression for the causal set d'Alembertian
• A 2D model of Causal Set Quantum Gravity: The emergence of the continuum
• Finite Size Scaling in 2d Causal Set Quantum Gravity
• Causal Set Generator and Action Computer
• The Ising model coupled to 2d orders

Cited by in corpus (1)

• Observables for cyclic causal set cosmologies