Rényi entropy of zeta urns.

We calculate analytically the Rényi entropy for the zeta-urn model with a Gibbs measure definition of the microstate probabilities. This allows us to obtain the singularities in the Rényi entropy from those of the thermodynamic potential, which is directly related to the free-energy density of the model. We enumerate the various possible behaviors of the Rényi entropy and its singularities, which depend on both the value of the power law in the zeta urn and the order of the Rényi entropy under consideration.

Random allocation models in the thermodynamic limit.

We discuss the phase transition and critical exponents in the random allocation model (urn model) for different statistical ensembles. We provide a unified presentation of the statistical properties of the model in the thermodynamic limit, uncover relationships between the thermodynamic potentials, and fill some lacunae in previous results on the singularities of these potentials at the critical point and behavior in the thermodynamic limit. The presentation is intended to be self-contained, so we carefully derive all formulas step by step throughout. Additionally, we comment on a quasiprobabilistic normalization of configuration weights, which was considered in some recent studies.

(Four) Dual Plaquette 3D Ising Models.

A characteristic feature of the 3 d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the 3 d plaquette Ising and the X-Cube model is similar to that between the 2 d quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the 2 d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the 3 d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3 d plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin-Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.

Damage spreading in small world Ising models.

We study damage spreading in the ferromagnetic Ising model on small world networks using Monte Carlo simulation with Glauber dynamics. The damage spreading temperature T(d) is determined as a function of rewiring probability p for small world networks obtained by rewiring the two-dimensional square and three dimensional cubic lattices. We find that the damage for different values of p collapse onto master curves when plotted against a rescaled temperature and that the distance between T(d) and the critical temperature T(c) increases with p. We argue that when using the Ising model to study social systems, it is necessary to place the spins on a small world network rather than on a regular lattice.