The Ising model coupled to 2d orders

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.

25 pages, 28 figures

References in corpus (15)

• The Scalar Curvature of a Causal Set
• Discreteness without symmetry breaking: a theorem
• Causal set d'Alembertians for various dimensions
• Particle propagators on discrete spacetime
• A new perspective on matter coupling in 2d quantum gravity
• A Distinguished Vacuum State for a Quantum Field in a Curved Spacetime: Formalism, Features, and Cosmology
• Generalized Causal Set d'Alembertians
• Towards a Definition of Locality in a Manifoldlike Causal Set
• Fourth-Order Cumulants to Characterize the Phase Transitions of a Spin-1 Ising Model
• Nonlocal Scalar Quantum Field Theory from Causal Sets
• 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
• Tests of Quantum Gravity-Induced Non-Locality via Opto-mechanical Experiments
• Off-shell Dark Matter: A Cosmological relic of Quantum Gravity

Cited by in corpus (5)

• The causal set approach to quantum gravity
• Predictive power of grand unification from quantum gravity
• A curvature bound from gravitational catalysis in thermal backgrounds
• Configuration space for quantum gravity in a locally regularized path integral
• Phase transitions in 2d orders coupled to the Ising model