Abstract We study the Glauber dynamics of a two dimensional Blume-Capel model (or dilute Ising model) with Kac potential parametrized by (β, θ) the “inverse temperature” and the “chemical potential”. We prove that the locally averaged spin field rescales to the solution of the dynamical Φ4 equation near a curve in the (β, θ) plane and to the solution of the dynamical Φ6 equation near one point ...

We extend the former matrix rearrangement approach of the entangling power to the general cases, without requirement of same dimensions of the subsystems. The entangling power of a unitary operator is completely determined by its realignment and partial transposition. As applications, we calculate the entangling power for the Ising interaction and the isotropic Heisenberg interaction in the hyb...

A generalized gauge invariant Ising model on random surfaces with non-trivial topology is proposed and investigated with the dual transformation. It is proved that the model is self-dual in case of a self-dual lattice. In special cases the model reduces to the known solvable Ising-type models.

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an N ×N box, with boundary conditions which are “plus” except for small regions at the corners which are either free or “minus.” The spectral gap decreases exponentially in the size of the corner regions, when these regions are of size at least of order logN . This means that removing as few as O(...

We consider the Ising model with external eld h and coupling constant J on an innnite connected graph G with uniformly bounded degree. We prove that if G is nonamenable, then the Ising model exhibits phase transition for some h 6 = 0 and some J < 1. On the other hand, if G is amenable and quasi{transitive, then phase transition cannot occur for h 6 = 0. In particular, a group is nonamenable if ...

A recently introduced model describing the folding of the triangular lattice is generalized allowing for defects in the lattice and written as an Ising model with nearest– neighbor and plaquette interactions on the honeycomb lattice. Its phase diagram is determined in the hexagon approximation of the cluster variation method and the crossover from the pure Ising to the pure folding model is inv...

For the Ising model, the spin magnetization transition is equivalent to the percolation transition of Fortuin-Kasteleyn clusters; this result remains valid also for the conventional continuous spin Ising model. The investigation of more general continuous spin models may help to obtain a percolation formulation for the critical behaviour in SU(2) gauge theory. We therefore study a broad class o...

We study the approximability of computing the partition function for ferromagnetic two-state spin systems. The remarkable algorithm by Jerrum and Sinclair showed that there is a fully polynomial-time randomized approximation scheme (FPRAS) for the special ferromagnetic Ising model with any given uniform external field. Later, Goldberg and Jerrum proved that it is #BIS-hard for Ising model if we...

We prove some inequalities for two-point correlations of Ising antiferromagnets and derive inequalities relating correlations of ferromagnets to correlations of antiferromagnets whose interactions and field strengths have equal magnitudes. The proofs are based on the method of duplicate spin variables introduced by J. Percus and used by several authors (Refs. 3-8) to derive correlation inequali...