Search results for "Ising Model"
showing 10 items of 241 documents
Theory of orientational glasses models, concepts, simulations
1992
Abstract This review describes the various attempts to develop a theoretical understanding for ordering and dynamics of randomly diluted molecular crystals, where quadrupole moments freeze in random orientations upon lowering the temperature, as a result of randomness and competing interactions. While some theories attempt to model this freezing into a phase with randomly oriented quadrupole moments in terms of a bond-disorder concept analogous to the Edwards-Anderson model of spin glasses, other theories attribute the freezing to random field-like terms in the Hamiltonian. While models of the latter type have been studied primarily by microscopic molecular field-type treatments, the former…
The four dimensional Ising spin glass: A Monte Carlo study (invited)
1991
We describe results of Monte Carlo simulation studies on the Ising spin glass in four dimensions on a hypercubic lattice with nearest neighbor bonds. Studies of the equilibrium static properties show that the system undergoes a genuine phase transition to an ordered spin glass phase. Critical dynamical behavior is analyzed to obtain the dynamic exponent. Finally, we describe results on the spin glass phase, in particular the finite size scaling of the order parameter distribution function, and compare it with existing models of the spin glass phase, namely the droplet model and the Parisi solution for the low temperature phase of the infinite range spin glass.
Rounding of Phase Transitions in Cylindrical Pores
2010
Phase transitions of systems confined in long cylindrical pores (capillary condensation, wetting, crystallization, etc.) are intrinsically not sharply defined but rounded. The finite size of the cross section causes destruction of long range order along the pore axis by spontaneous nucleation of domain walls. This rounding is analyzed for two models (Ising/lattice gas and Asakura-Oosawa model for colloid-polymer mixtures) by Monte Carlo simulations and interpreted by a phenomenological theory. We show that characteristic differences between the behavior of pores of finite length and infinitely long pores occur. In pores of finite length a rounded transition occurs first, from phase coexiste…
Critical Wetting and Interface Localization—Delocalization Transition in a Double Wedge
2004
Using Monte Carlo simulations and finite-size scaling methods we study “wetting” in Ising systems in a L x L x L y pore with quadratic cross section. Antisymmetric surface fields H s act on the free L x L y surfaces of the opposing wedges, and periodic boundary conditions are applied along the y-direction. Our results represent the first simulational observation of fluctuation effects in three dimensional wetting phenomena and corroborate recent predictions on wedge filling. In the limit L → ∞ L y /L 3 = const the system exhibits a new type of phase transition, which is the analog of the “filling transition” that occurs in a single wedge. It is characterized by critical exponents α = 3/4, β…
A Note on the algebraic approach to the «almost» mean-field Heisenberg model
1993
We generalize to an «almost» mean-field Heisenberg model the algebraic approach already formulated for Ising models. We show that there exists a family of «relevant» states on which the algebraic dynamics αt can be defined. © 1993 Società Italiana di Fisica.
The mean field to Ising crossover in the critical behavior of polymer mixtures : a finite size scaling analysis of Monte Carlo simulations
1993
Monte Carlo simulations of the bond fluctuation model of symmetrical polymer mixtures (chain lengths N A =N B =N) are analyzed near the critical temperature T c (N) of their unmixing transition. Two choices of interaction range are studied, using a square-well potential with effective coordination number z eff ≃ 14 or z eff ≃ 5, respectively, at a volume fraction O= 0.5 of occupied lattice sites, and chain lengths in the range 8≤ N≤ 512. A linear relation between N and T c (N) is established, T c (N)= AN+B, where the correction term B is positive for z eff = 14 but negative for z eff = 5. The critical behavior of the models is analyzed via finite size scaling techniques, paying attention to…
The Ising–Bloch transition in degenerate optical parametric oscillators
2003
Domain walls in type I degenerate optical parametric oscillators are numerically investigated. Both steady Ising and moving Bloch walls are found, bifurcating one into another through a nonequilibrium Ising--Bloch transition. Bloch walls are found that connect either homogeneous or roll planforms. Secondary bifurcations affecting Bloch wall movement are characterized that lead to a transition from a steady drift state to a temporal chaotic movement as the system is moved far from the primary, Ising--Bloch bifurcation. Two kinds of routes to chaos are found, both involving tori: a usual Ruelle-Takens and an intermittent scenarios.
Critical phenomena in polymer mixtures: Monte Carlo simulation of a lattice model
1987
A lattice model of a symmetrical binary (AB) polymer mixture is studied, modelling the polymer chains by self-avoiding walks withN A =N B =N steps on a simple cubic lattice. If a pair of nearest neighbour sites is taken by different monomersAB orBA, an energye ab is won; if the pair of sites is taken by anAA or aBB pair, an energye is won, while the energy is reduced to zero if at least one of the sites of the pair is vacant. To allow enough chain mobility, 20% of the lattice sites are vacancies. In addition to local motions of the chain segments we use a novel “grand-canonical” simulation technique:A chains are transformed intoB chains and vice versa, keeping the chemical potential differe…
Phase Equilibria of Lattice Polymers from Histogram Reweighting Monte Carlo Simulations
1998
Histogram-reweighting Monte Carlo simulations were used to obtain polymer / solvent phase diagrams for lattice homopolymers of chain lengths up to r=1000 monomers. The simulation technique was based on performing a series of grand canonical Monte Carlo calculations for a small number of state points and combining the results to obtain the phase behavior of a system over a range of temperatures and densities. Critical parameters were determined from mixed-field finite-size scaling concepts by matching the order parameter distribution near the critical point to the distribution for the three-dimensional Ising universality class. Calculations for the simple cubic lattice (coordination number z…
Quench of symmetry broken ground states
2016
We analyze the problem of how different ground states associated to the same set of the Hamiltonian parameters evolve after a sudden quench. To realize our analysis we define a quantitative approach to the local distinguishability between different ground states of a magnetically ordered phase in terms of the trace distance between the reduced density matrices obtained projecting two ground states in the same subset. Before the quench, regardless the particular choice of the subset, any system in a magnetically ordered phase is characterized by ground states that are locally distinguishable. On the other hand, after the quench, the maximum of the distinguishability shows an exponential deca…