Three-dimensional ising model in the fixed-magnetization ensemble: A monte carlo study (original) (raw)
Related papers
The magnetization of the 3D Ising model
Journal of Physics A: Mathematical and General, 1996
We present highly accurate Monte Carlo results for simple cubic Ising lattices containing up to 256 3 spins. These results were obtained by means of the Cluster Processor, a newly built special-purpose computer for the Wolff cluster simulation of the 3D Ising model. We find that the magnetization M(t) is perfectly described by M(t) = (a 0 − a 1 t θ − a 2 t)t β , where t = (T c − T )/T c , in a wide temperature range 0.0005 < t < 0.26. If there exist corrections to scaling with higher powers of t, they are very small. The magnetization exponent is determined as β = 0.3269 (6). An analysis of the magnetization distribution near criticality yields a new determination of the critical point: K c = J/k B T c = 0.2216544, with a standard deviation of 3·10 −7 .
Physical Review E, 2021
A cluster weight Ising model is proposed by introducing an additional cluster weight in the partition function of the traditional Ising model. It is equivalent to the O(n) loop model or ncomponent face cubic loop model on the two-dimensional lattice, but on the three-dimensional lattice, it is still not very clear whether or not these models have the same universality. In order to simulate the cluster weight Ising model and search for new universality class, we apply a cluster algorithm, by combining the color-assignation and the Swendsen-Wang methods. The dynamical exponent for the absolute magnetization is estimated to be z = 0.45(3) at n = 1.5, consistent with that by the traditional Swendsen-Wang methods. The numerical estimation of the thermal exponent yt and magnetic exponent ym, show that the universalities of the two models on the three dimensional lattice are different. We obtain the global phase diagram containing paramagnetic and ferromagnetic phases. The phase transition between the two phases are second order at 1 ≤ n < nc and first order at n ≥ nc, where nc ≈ 2. The scaling dimension yt equals to the system dimension d when the first order transition occurs. Our results are helpful in the understanding of some traditional statistical mechanics models.
Journal of Physics A: Mathematical and General, 2004
Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T → 0), the size of the system going to infinity (N → ∞) while N [1 − tanh(J/kB T )] is kept finite (J being the nearest neighbor coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.
Statistical mechanics of the cluster Ising model
Physical Review A, 2011
We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.
Local and cluster critical dynamics of the 3d random-site Ising model
Physica A: Statistical Mechanics and its Applications, 2006
We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the Swendsen-Wang and Wolff cluster algorithms. The lattice sizes of L = 10 − 96 are analysed by a finite-size-scaling technique. The site dilution concentration p = 0.85 was chosen to minimize the correction-to-scaling effects. We calculate numerical values of the dynamical critical exponents for the integrated and exponential autocorrelation times for energy and magnetization. As expected, cluster algorithms are characterized by lower values of dynamical critical exponent than the local one: also in the case of dilution critical slowing down is more pronounced for the Metropolis algorithm. However, the striking feature of our estimates is that they suggest that dilution leads to decrease of the dynamical critical exponent for the cluster algorithms. This phenomenon is quite opposite to the local dynamics, where dilution enhances critical slowing down.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000
We study the probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point. The systems under consideration are the 3-dimensional Ising model on a simple cubic lattice, and its 3-state generalization known to have remarkably small corrections to scaling. Both models are studied in a cubic box with periodic boundary conditions. The model with reduced corrections to scaling makes it possible to determine P(M) with unprecedented precision. We also obtain a simple, but remarkably accurate, approximate formula describing the universal shape of P(M).
Equilibrium cluster distributions of the three-dimensional Ising model in the one phase region
1983
Abstract We analyse equilibrium cluster distributions obtained numerically from a ferromagnetic Ising model (simple cubic lattice, 125000 sites and periodic boundary conditions) along the coexistence line and in the one-phase region below T c. We find evidences that the distribution of sizes and energies scales with temperature and external magnetic field giving Binder's droplet exponent y≈ 4/9.
Ground-state numerical study of the three-dimensional random-field Ising model
Physical Review B, 2003
The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to 60^3. For each realization of the normalized random fields, the strength of the random field, Delta and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the H-Delta plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents and both exponents are found to be near zero.
Physical Review E, 1999
The equilibrium ensemble approach to disordered systems is used to investigate the critical behaviour of the two dimensional Ising model in presence of quenched random site dilution. The numerical transfer matrix technique in semi-infinite strips of finite width, together with phenomenological renormalization and conformal invariance, is particularly suited to put the equilibrium ensemble approach to work. A new method to extract with great precision the critical temperature of the model is proposed and applied. A more systematic finite-size scaling analysis than in previous numerical studies has been performed. A parallel investigation, along the lines of the two main scenarios currently under discussion, namely the logarithmic corrections scenario (with critical exponents fixed in the Ising universality class) versus the weak universality scenario (critical exponents varying with the degree of disorder), is carried out. In interpreting our data, maximum care is constantly taken to be open in both directions. A critical discussion shows that, still, an unambiguous discrimination between the two scenarios is not possible on the basis of the available finite size data.