Related papers: Cluster Percolation in the Two-Dimensional Ising S…
It is shown, by means of Monte Carlo simulation and Finite Size Scaling analysis, that the Heisenberg spin glass undergoes a finite-temperature phase transition in three dimensions. There is a single critical temperature, at which both a…
We study spin glass behavior in a random Ising Coulomb antiferromagnet in two and three dimensions using Monte Carlo simulations. In two dimensions, we find a transition at zero temperature with critical exponents consistent with those of…
The two-dimensional (zero magnetic field) Ising model is known to undergo a second order para-ferromagnetic phase transition, which is accompanied by a correlated percolation transition for the Fortuin-Kasteleyn (FK) clusters. In this paper…
In an artificial 3D percolation nano medium, the clusters filled by the Ising magnets give rise to a topologically nontrivial magnetic structure, leading to new features of the ferromagnetic phase transition without an external magnetic…
Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temperatures below $T_{\rm c}$ and, in analogy with a recent model of dense colloidal suspensions,interpreted in terms of clusters of contiguous…
Ordering of the Heisenberg spin glass with the nearest-neighbor Gaussian coupling is investigated by equilibrium Monte Carlo simulations in four and five dimensions. Ordering of the mean-field Heisenberg spin-glass is also studied for…
The fractal dimensions and the percolation exponents of the geometrical spin clusters of like sign at criticality, are obtained numerically for an Ising model with temperature-dependent annealed bond dilution, also known as the thermalized…
We recently showed that the two-dimensional Ising spin glass allows for a line of renormalization group fixed points which explains properties observed in numerical studies. We observe that this exact result corresponds to enhancement to a…
Ordering of the three-dimensional Heisenberg spin glass with Gaussian coupling is studied by extensive Monte Carlo simulations. The model undergoes successive chiral-glass and spin-glass transitions at nonzero temperatures T_{CG} > T_{SG} >…
Spin and chirality orderings of a three-dimensional XY spin glass are studied by extensive Monte Carlo simulations. By calculating an appropriately defined spin-overlap distribution function, we show that the finite-temperature chiral-glass…
Despite the extreme simplicity in their definition, spin glasses disclose a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis we try to shed light on some of them, focusing on one hand on the search of…
Two dimensional (2D) classical system of dipole particles confined by a quadratic potential is studied. For clusters of N < 81 particles ground state configurations and appropriate eigenfrequencies and eigenvectors for the normal modes are…
In magnetic materials, spins sometimes freeze into spatially disordered glassy states. Glass forming liquids or structural glasses are found very often in three dimensions. However, in two dimensions(2D) it is believed that both spin glass…
Via Monte Carlo studies of the frustrated XY or classical planar model we demonstrate the possibility of a finite (nonzero) temperature spin/gauge glass phase in two dimensions. Examples of both periodic and quasiperiodic two dimensional…
Geometric representations provide a useful perspective on critical phenomena in the Ising model. In a recent study [Phys. Rev. E 112, 034118 (2025)], we found that the two-dimensional critical Ising model exhibits two consecutive…
Via extensive Monte Carlo studies we show that the frustrated XY Hamiltonian on a 2-D Penrose lattice admits of a spin glass phase at low temperature. Studies of the Edwards-Anderson order parameter, spin glass susceptibility, and local…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
Results from Monte Carlo simulations of the two-dimensional gauge glass supporting a zero-temperature transition are presented. A finite-size scaling analysis of the correlation length shows that the system does not exhibit spin-glass order…
Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, the Ising model on multiplex networks with two layers is considered,…
We examine the geometrical and topological properties of surfaces surrounding clusters in the 3--$d$ Ising model. For geometrical clusters at the percolation temperature and Fortuin--Kasteleyn clusters at $T_c$, the number of surfaces of…