Related papers: Finite-Size Scaling of the High-Dimensional Ising …
Field-theoretical calculations predict that, at the upper critical dimension $d_c=4$, the finite-size scaling (FSS) behaviors of the Ising model would be modified by multiplicative logarithmic corrections with thermal and magnetic…
Recently, we argued [Chin. Phys. Lett. $39$, 080502 (2022)] that the Ising model simultaneously exhibits two upper critical dimensions $(d_c=4, d_p=6)$ in the Fortuin-Kasteleyn (FK) random-cluster representation. In this paper, we perform a…
We present a Monte Carlo study of the Fortuin-Kasteleyn (FK) clusters of the Ising model on the square (2D) and simple-cubic (3D) lattices. The wrapping probability, a dimensionless quantity characterizing the topology of the FK clusters on…
The exact solution of the Ising model on the complete graph (CG) provides an important, though mean-field, insight for the theory of continuous phase transitions. Besides the original spin, the Ising model can be formulated in the…
We derive the exact actions of the $Q$-state Potts model valid on any graph, first for the spin degrees of freedom, and second for the Fortuin-Kasteleyn clusters. In both cases the field is a traceless $Q$-component scalar field…
We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size L as L^{5/4}, rather than proportional to L as in standard finite size scaling (FSS) theory. Our results confirm a…
The upper critical dimension of the Ising model is known to be $d_c=4$, above which critical behavior is regarded as trivial. We hereby argue from extensive simulations that, in the random-cluster representation, the Ising model…
The fractal structure and scaling properties of a 2d slice of the 3d Ising model is studied using Monte Carlo techniques. The percolation transition of geometric spin (GS) clusters is found to occur at the Curie point, reflecting the…
The Fortuin-Kasteleyn (FK) random cluster model, which can be exactly mapped from the $q$-state Potts spin model, is a correlated bond percolation model. By extensive Monte Carlo simulations, we study the FK bond representation of the…
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…
The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension $d=2$ to 7 with periodic boundary conditions. The critical exponents associated to the Finite-Size Scaling of the magnetic susceptibility are…
We study the three-dimensional (3D) bond-diluted Edwards-Anderson (EA) model with binary interactions at a bond occupation of 45% by Monte Carlo (MC) simulations. Using an efficient cluster MC algorithm we are able to determine the…
We propose a method to obtain an improved Hamiltonian (action) for the Ising universality class in three dimensions. The improved Hamiltonian has suppressed leading corrections to scaling. It is obtained by tuning models with two coupling…
We apply a worm algorithm to simulate the quantum transverse-field Ising model in a path-integral representation of which the expansion basis is taken as the spin component along the external-field direction. In such a representation, a…
The corrections to finite-size scaling in the critical two-point correlation function G(r) of 2D Ising model on a square lattice have been studied numerically by means of exact transfer-matrix algorithms. The systems have been considered,…
The two-dimensional Potts model can be studied either in terms of the original Q-component spins, or in the geometrical reformulation via Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for arbitrary real values of…
We present an extensive Markov-chain Monte Carlo study of the finite-size scaling behavior of the Fortuin-Kasteleyn Ising model on five-dimensional hypercubic lattices with periodic boundary conditions. We observe that physical quantities,…
In finite-size scaling analyses of critical phenomena, proper consideration of correction terms, which can come from different sources, plays an important role. For the Fortuin-Kasteleyn representation of the $Q$-state Potts model in two…
Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of Statistical Physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In…
Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it…