Related papers: Using memory to identify phase transitions on a Ca…
The spectral statistics of a Cayley-tree is numerically studied. The statistics are non-universal due to the high ratio of boundary sites. Once the boundary sites are connected to each other in a way that preserves the local structure of…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
We study phase transitions in the Ising model on random graphs using graph limits. We show that the critical temperatures are determined by the eigenvalues of the kernel operator associated with the graph limit. Bifurcation diagrams for…
Using Monte Carlo histogram methods, the microcanonical caloric curve is computed for the Ising model in two and three dimensions with fixed magnetization. Whereas the signatures of a first order phase transition are clearly visible for…
Since the landmark work of Lee and Yang, locating the zeros of the partition function in the complex magnetic-field plane has become a powerful method for studying phase transitions. Fisher later extended this approach to complex…
Monte Carlo simulations are performed for the S = 1/2 XY and ferro- and antiferromagnetic Heisenberg model in two dimensions using the loop algorithm. Thermodynamic properties of all these models are investigated in wide temperature range.…
Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator…
Van der Waals "sliding" ferroelectric bilayers, whose electric polarization is locked to the interlayer alignment, show promise for future non-volatile memory and other nanoelectronic devices. These applications require a fuller…
We have investigated by Monte-Carlo simulation the phase diagram of a three-dimensional Ising model with nearest-neighbor ferromagnetic interactions and small, but long-range (Coulombic) antiferromagnetic interactions. We have developed an…
The two-dimensional Ising model with nearest-neighbor ferromagnetic and long-range dipolar interactions exhibits a rich phase diagram. The presence of the dipolar interaction changes the ferromagnetic ground state expected for the pure…
We present a simple model that recalls two different patterns depending on the temperature. To realize a change in recall pattern due to temperature change, we embed two patterns to different graphs: the first pattern into a fully connected…
We consider the Ising model on a Cayley tree of order two with nearest neighbor interactions and competing next nearest neighbor interactions restricted to spins belonging to the same branch of the tree. This model was studied by Vannimenus…
We consider the 2D $J_1-J_2$ classical XY model on a square lattice. In the frustrated phase corresponding to $J_2>J_1/2$, an Ising like order parameter emerges by an ``order due to disorder'' effect. This leads to a discrete $Z_2$ symmetry…
Within the framework of mean field theory, we examine the phase transitions in Ising magnetic films and superlattices. By transfer matrix method, we derive two general nonlinear equations for phase transition temperatures of Ising magnetic…
The nature of freezing and melting transitions for a system of hard disks in a spatially periodic external potential is studied using extensive Monte Carlo simulations. Detailed finite size scaling analysis of various thermodynamic…
We study analytically the effect of temperature cyclings in mean-field spin-glasses. In accordance with real experiments, we obtain a strong reinitialization of the dynamics on decreasing the temperature combined with memory effects when…
Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a…
Using Monte Carlo simulations we study cooling-rate effects in a three-dimensional Ising model with four-spin interaction. During coarsening, this model develops growing energy barriers which at low temperature lead to very slow dynamics.…
Fourth-order cumulants of physical quantities have been used to characterize the nature of a phase transition. In this paper we report some Monte Carlo simulations to illustrate the behavior of fourth-order cumulants of magnetization and…
We use Monte Carlo simulations to study the one-dimensional long-range diluted Heisenberg spin glass with interactions that fall as a power, sigma, of the distance. Varying the power is argued to be equivalent to varying the space dimension…