TL;DR
This paper simulates the Ising model on dynamical quadrangulations to confirm universality of KPZ/DDK exponents and investigates antiferromagnetic transitions on bipartite dynamical lattices.
Contribution
It introduces a generalized flip move for quadrangulations and explores the Ising antiferromagnet transition on a dynamical bipartite lattice.
Findings
Confirmed universality of KPZ/DDK exponents for the Ising transition
Defined a staggered magnetization for antiferromagnetic analysis
Observed the antiferromagnetic transition on a dynamical bipartite lattice
Abstract
We simulate the Ising model on dynamical quadrangulations using a generalization of the flip move for triangulations with two aims: firstly, as a confirmation of the universality of the KPZ/DDK exponents of the Ising phase transition, worthwhile in view of some recent surprises with other sorts of dynamical lattices; secondly, to investigate the transition of the Ising antiferromagnet on a dynamical loosely packed (bipartite) lattice. In the latter case we show that it is still possible to define a staggered magnetization and observe the antiferromagnetic analogue of the transition.
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