Monte Carlo renormalization group study of first order phase transitions

The two-lattice matching MCRG method is used to study first order phase transitions. While the method gives the critical exponent in agreement with the predicted value 1/d, where d is the dimension of the system, it indicates discontinuous flows on the phase transition surface.     

Monte Carlo simulation of metallic spin glasses

We discuss a numerical simulation of the Ising model on a three-dimensional random lattice. Calculations were made of the low-temperature susceptibility per spin and specific heat per spin using the Monte Carlo technique for the SG system CuMn with different concentrations.     

Monte Carlo methods for the study of phase transitions and phase equilibria

Monte Carlo methods can predict macroscopic properties of N-body systems from the (classical) Hamiltonian describing the interactions between the particles and hence can serve as a basic tool of equilibrium statistical mechanics, avoiding uncontrolled approximations. However, a necessary ingredientis the control of finite size effects. For this purpose, the finite size scaling analysis of suitable distribution functions is a powerful tool. The basic ideas of this approach will be discussed, including extensions to critical phenomena where the hyperscaling relation between critical exponents is violated (colloid-polymer mixtures in random media as a realization of the random field Ising model, phase transitions caused by competition of interfacial and surface effects, etc.) Finite size effects on two-phase coexistence cause the existence of a van-der-Waals-like loop, but it has a completely different origin, the “spinodal” reflecting the “droplet evaporation/condensation” transition. Also the possibility to extract interface free energies is discussed.     

Monte Carlo simulation of a three-dimensional spin glass

Similarly to two dimensions, the Edwards-Anderson model of (Ising) spins with a Gaussian nearest-neighbor exchange-force distribution gives near $\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{≈1.5}\text{ΔJ}\text{k}{}_{\mathrm{<mtext>B</mtext>}}$ a cusp in the susceptibility, a peak in the specific heat, and a continuous vanishing of the “order parameter”.     

Monte Carlo study of very weakly first-order transitions in the three-dimensional Ashkin-Teller model

We propose numerical simulations of the Ashkin-Teller model as a foil for theoretical techniques for studying very weakly first-order phase transitions in three dimensions. The Ashkin-Teller model is a simple two-spin model whose parameters can be adjusted so that it has an arbitrarily weakly first-order phase transition. In this limit, there are quantities characterizing the first-order transition which are universal: we measure the relative discontinuity of the specific heat, the correlation length, and the susceptibility across the transition by Monte Carlo simulation.     

Monte Carlo studies of finite-size effects at first-order transitions

First-order phase transitions are ubiquitous in nature but their presence is often uncertain because of the effects which finite size has on all transitions. In this article we consider a general treatment of size effects on lattice systems with discrete degrees of freedom and which undergo a first-order transition in the thermodynamic limit. We review recent work involving studies of the distribution functions of the magnetization and energy at a first-order transition in a finite sample of size N connected to a bath of size N′. Two cases: N′ = ∞ and N′ = finite are considered. In the former (canonical ensemble) case, the distributions are approximated by a superposition of Gaussians corresponding to the different phases; all finite-size effects then vary as N or 1/N. The latter case involves the Gaussian ensemble where the entropy of the bath has a convenient form; for small N′, first-order transitions are characterized by van der Waals' loops in (for example) the energy vs. temperature curves. Results from extensive Monte Carlo simulations of Ising and Potts models in d = 2 are presented to confirm the predictions. Comparison is made with data from second-order transitions to show that the order of a transition can be distinguished through such studies, although problems still occur for first-order transitions very close to critical points.     

Monte Carlo simulation of DNMR spectra of coupled spin systems

A new program MC-DNMR is presented for the simulation of dynamic nuclear magnetic resonance spectra. The algorithm is a Monte Carlo type method based on the extension of single spin vector model to coupled spin systems. This extension is explained in detail and the theory is justified by examples. The main advantage of this program is the significantly smaller sizes of matrices than that in programs based on density matrix theory. So spectra of systems can be simulated that was impossible previously.     

Monte Carlo simulation of pressure-induced phase transitions in spin-crossover materials

Pressure-induced phase transitions of spin-crossover materials are studied in a microscopic model taking into account the elastic interaction among distortions of lattice due to the difference of the molecular sizes between the high-spin state and the low-spin state. We perform Monte Carlo simulations in the constant pressure ensemble and reproduce several important properties of the pressure effect in a unified way with a microscopic mechanism for the first time. The simulation newly reveals how the temperature dependence of the ordering process changes with the pressure.     

Monte Carlo simulation of magnetic phase transitions in Mn-doped ZnO

The magnetic properties of Mn-doped ZnO semiconductor have been investigated using the Monte Carlo method within the Ising model. The temperature dependences of the spontaneous magnetization, specific heat and magnetic susceptibility have been constructed for different concentrations of magnetic dopant Mn and different carrier concentrations. The exact values of Mn concentration and carrier concentration at which high temperature transition occurs are determined. An alternative for the explanation of some controversies concerning the existence and the nature of magnetism in Mn diluted in ZnO systems is given. Other features are also studied.