Related papers: Approach to Fixation for Zero-Temperature Stochast…
Hard constraints imposed in statistical mechanics models can lead to interesting thermodynamical behaviors, but may at the same time raise obstructions in the thoroughfare to thermal equilibration. Here we study a variant of Baxter's…
We consider the Glauber dynamics of a ferromagnetic Ising-Kac model on a three-dimensional periodic lattice of size $(2N + 1)3$, in which the flipping rate of each spin depends on an average field in a large neighborhood of radius…
A ``persistence'' exponent theta has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: for zero-temperature homogeneous Ising models on the d-dimensional cubic lattice, the fraction p(t)…
The geometric frustration of the spin-1/2 Ising-Heisenberg model on the triangulated Kagome (triangles-in-triangles) lattice is investigated within the framework of an exact analytical method based on the generalized star-triangle mapping…
We study the magnetization for the classical antiferromagnetic Ising model on the Shastry-Sutherland lattice using the tensor renormalization group approach. With this method, one can probe large spin systems with little finite-size effect.…
We study the low-temperature physics of the $SU(2)$-symmetric spin-$1/2$ Heisenberg antiferromagnet on a pyrochlore lattice and find fingerprint evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are…
The free energy and the specific heat of the two-dimensional Gaussian random bond Ising model on a square lattice are found with high accuracy using graph expansion method. At low temperatures the specific heat reveals a zero-temperature…
We study the metastability of the ferromagnetic Ising model on a random $r$-regular graph in the zero temperature limit. We prove that in the presence of a small positive external field the time that it takes to go from the all minus state…
We consider the continuous time, zero-temperature heat-bath dynamics for the nearest-neighbor Ising model on $Z^2$ with positive magnetic field. For a system of size $L\in N$, we start with initial condition $\sigma$ such that $\sigma_x=-1$…
The ferromagnetic Ising model on an $n\times n$ square lattice region $\Lambda$ with mixed boundary conditions can exhibit a phase transition as temperature varies. For this spin system, if we fix the spins on the top and bottom sides of…
Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice with Heisenberg intra-dimer and Ising inter-dimer couplings are found by two independent rigorous procedures. The first method uses a unitary…
We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified…
We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an…
We consider the phase ordering problem for the low-temperature Ising dynamics initialized from a biased and disordered initialization. Work of Fontes, Schonmann, Sidoravicius (2002) showed that at zero-temperature, Ising Glauber dynamics on…
An asymmetrical 2D Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice,…
We construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We…
We investigate non-equilibrium properties of the frustrated Heisenberg antiferromagnets on the triangular lattice. Nonequilibrium critical relaxation of frustrated Heisenberg antiferromagnets shows a dynamic transition (or, at least, sharp…
We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of +1 or -1 to each site in ${\bf Z}^2$, is the…
We investigate the interplay of classical degeneracy and quantum dynamics in a range of periodic frustrated transverse field Ising systems at zero temperature. We find that such dynamics can lead to unusual ordered phases and phase…
We study the zero-temperature criticality of the Ising model on two-dimensional dynamical triangulations to contemplate its physics. As it turns out, an inhomogeneous nature of the system yields an interesting phase diagram and the physics…