Tests for Monte Carlo renormalization studies on Ising models

In this expanded version of an earlier letter, we consider many computational details that were omitted for want of space. Ford = 2 Ising spins with up to 13 different short-range interactions, we construct the critical surface in the vicinity of (Onsager's) nearest-neighbor (nn) critical point by using the body of the available information on the solvable nn case. We then see if the Monte Carlo renormalization group flows generated from this point do indeed lie on this surface and quantify the errors if they do not.     

Monte Carlo simulations of ferromagnetism in p-Cd1-xMnxTe quantum wells

Monte Carlo simulations, in which the Schr?dinger equation is solved at each Monte Carlo sweep, are employed to assess the influence of magnetization fluctuations, short-range antiferromagnetic interactions, disorder, magnetic polaron formation, and spin-Peierls instability on the carrier-mediated Ising ferromagnetism in two-dimensional electronic systems. The determined critical temperature and hysteresis are affected in a nontrivial way by the antiferromagnetic interactions. The findings explain striking experimental results for modulation-doped p-Cd1-xMnxTe quantum wells.     

Critical Temperature of Periodic Ising Models

A periodic Ising model has interactions which are invariant under translations of a full-rank sublattice of . We prove an exact, quantitative characterization of the critical temperature, defined as the supremum of temperatures for which the spontaneous magnetization is strictly positive. For the ferromagnetic model, the critical temperature is the solution of a certain algebraic equation, resulting from the condition that the spectral curve of the corresponding dimer model on the Fisher graph has a real zero on the unit torus. With our technique we provide a simple proof for the exponential decay of spin-spin correlations above the critical temperature, as well as the exponential decay of the edge-edge correlations for all non-critical edge weights of the corresponding dimer model on periodic Fisher graphs.     

Phase diagrams of spin-1 Ising model with bilinear and quadrupolar interactions under magnetic field. Two-particle cluster approximation

The spin-1 Ising model with bilinear and quadrupolar short-range interactions under magnetic field is investigated within the two-particle cluster approximation. It is shown that for those values of the quadrupolar interaction when at zero magnetic field the system undergoes a temperature phase transition between quadrupolar and paramagnetic phases, a triple point may exist in the temperature vs. magnetic field phase diagrams, necessarily along with a critical point. It is also shown that the critical points in the temperature vs. magnetic field phase diagrams of the investigated model can be of three types.     

Compressible Ising double chains

We obtain exact expressions for the free energy and the magnetic susceptibility in zero field of a compressible double Ising chain with first and second neighbour interactions. The chain is supposed to be made of rigid rods which move like dumbbells in an elastic harmonic potential. The exchange interactions along the direction of the chain are linear functions of the spacing between rods. The effective spin hamiltonian of the double chain involves short-range two and four-spin interactions. Due to the existence of compensation points, we obtain regions of peculiar thermodynamic properties in the pressure-temperature phase diagram.     

A Note on Exponential Decay in the Random Field Ising Model

For the two-dimensional random field Ising model (RFIM) with bimodal (i.e., two-valued) external field, we prove exponential decay of correlations either (i) when the temperature is larger than the critical temperature of the Ising model without external field and the magnetic field strength is small or (ii) at any temperature when the magnetic field strength is sufficiently large. Unlike previous work on exponential decay, our approach is not based on cluster expansions but rather on arguably simpler methods; these combine an analysis of the Kertész line and a coupling of Ising measures (and also their random cluster representations) with different boundary conditions. We also show similar but weaker results for the RFIM with a general field distribution and in any dimension.     

Competition of percolation and phase separation in a fluid of adhesive hard spheres

Using a combination of Monte Carlo techniques, we locate the liquid-vapor critical point of adhesive hard spheres. We find that the critical point lies deep inside the gel region of the phase diagram. The (reduced) critical temperature and density are tau(c)=0.1133+/-0.0005 and rho(c)=0.508+/-0.01. We compare these results with the available theoretical predictions. Using a finite-size scaling analysis, we verify that the critical behavior of the adhesive hard sphere model is consistent with that of the 3D Ising universality class, the default for systems with short-range attractive forces.     

Crossover behavior in fluids with Coulomb interactions

According to extensive experimental findings, the Ginzburg temperature t_G for ionic fluids differs substantially from that of nonionic fluids [W. Schr?er, H. Weig?rtner, Pure Appl. Chem. 76, 19 (2004)]. A theoretical investigation of this outcome is proposed here by a mean field analysis of the interplay of short and long range interactions on the value of t_G. We consider a quite general continuous charge-asymmetric model made of charged hard spheres with additional short-range interactions (without electrostatic interactions the model belongs to the same universality class as the 3D Ising model). The effective Landau-Ginzburg Hamiltonian of the full system near its gas-liquid critical point is derived from which the Ginzburg temperature is calculated as a function of the ionicity. The results obtained in this way for t_G are in good qualitative and sufficient quantitative agreement with available experimental data.     

Microcanonical relation between continuous and discrete spin models

A relation between a class of stationary points of the energy landscape of continuous spin models on a lattice and the configurations of an Ising model defined on the same lattice suggests an approximate expression for the microcanonical density of states. Based on this approximation we conjecture that if a O(n) model with ferromagnetic interactions on a lattice has a phase transition, its critical energy density is equal to that of the n=1 case, i.e., an Ising system with the same interactions. The conjecture holds true in the case of long-range interactions. For nearest-neighbor interactions, numerical results are consistent with the conjecture for n=2 and n=3 in three dimensions. For n=2 in two dimensions (XY model) the conjecture yields a prediction for the critical energy of the Bere?inskij-Kosterlitz-Thouless transition, which would be equal to that of the two-dimensional Ising model. We discuss available numerical data in this respect.     

Exact results for a random frustrated Ising model on the Kagomé lattice

We perform a slight modification of the decoration-decimation transformation which allows us to map the homogeneous Ising model on the honeycomb lattice on an inhomogeneous Ising model on the Kagomé lattice. Then, we obtain exact results for a class of random bond Ising model on the Kagomé lattice with competing interactions and show that the different types of frustration make the critical point of the pure model disappear.     

Union Jack晶格上伊辛模型的自由费密近似解

运用自由费密近似对Union Jack晶格上具有各向异性二体耦合作用及三体相互作用的伊辛模型进行了求解,得到了模型的自由能、自发磁矩和临界点方程。在耦合常数简化为正方晶格上的伊辛模型时,得到了与Onsager一致的解。     

Critical behavior of uniaxial ferromagnetics with dipolar interactions

The critical behavior of uniaxial ferromagnets with exchange and dipolar interaction is studied by exact renormalization group techniques. A crossover occurs from short-range (Ising) to characteristic dipolar behavior, which is described.     

Elastic Ising-like model for the nucleation and domain formation in spin crossover molecular solids

We investigate the nucleation, domain formation and propagation mechanisms observed in Spin Crossover materials, in the framework of an Ising-like model taking into account the elastic nature of the interactions. In Spin Crossover materials, the intermolecular coupling originates from a volume difference between the High Spin and the Low Spin molecular states and is simulated by anharmonic interaction potentials whose strengths are molecular-state-dependent. Using Monte Carlo methods, the phase diagram has been established. We show that the model contains both Ising short-range couplings and long-range elastic interactions. In particular, the results of long-range elastic models are reproduced. The introduction of lattice dynamics leads to the existence of spatial distributions of interaction energy and crystal field, corresponding to a local definition of physical properties. The nucleation process becomes highly dependent on the structural inhomogeneities induced by the spin transition. In this approach, connections strength between neighboring molecules are no more equivalent and have different ability to propagate domains. The presence of short-range Ising couplings gives rise to the occurrence of strong bonds forming a volume in which domains of the daughter phase can grow; in this case a macroscopic phase separation appears during the first order transition, even in a system with periodic boundary conditions. By contrast, in the case of a model with only long-range elastic interactions; strong bonds are uniformly spread in the lattice and a homogeneous phase transformation is observed, in good agreement with previous theoretical investigations.     

Percolation transition in an irreversible-surface reaction model

Monte Carlo simulation studies of percolation transition in a surface reaction model describing the oxidation of carbon mono-oxide on a catalytic surface are presented. The percolation transition for adsorbed oxygen atoms occurs below the poisoning transition where carbon mono-oxide completely covers the surface of the catalyst and takes place for an oxygen coverage of about 0.525 which is close to the percolation transition in an Ising lattice gas with nearest-neighbor attractive interactions. In several respects the oxygen clusters near the percolation threshold resemble those of the Ising lattice gas near its critical point.     

Inverse problem of inhomogeneous ising models with many-spin interactions

We study the inverse problem of inhomogeneous Ising lattices with a general spin which consists in finding the external potential required to produce a given profile of equilibrium single-site distributions. In particular, we extend a previously developed two-step procedure for simplifying the inverse problem to the case of many-spin interactions. The general procedure is applied to a special chain withh-spin interactions for which the inverse problem is, in principle and forh=2, 3, 4 also in practice, solvable exactly. Direct correlation functions of the proposed model have only short-range support.     

Breaking of ergodicity and long relaxation times in systems with long-range interactions

The thermodynamic and dynamical properties of an Ising model with both short-range and long-range, mean-field-like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short-range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long-range interactions and are expected to be valid even when the interaction is slowly decaying with distance.     

Ising deconfinement transition between Feshbach-resonant superfluids

We investigate the phase diagram of bosons interacting via Feshbach-resonant pairing interactions in a one-dimensional lattice. Using large scale density matrix renormalization group and field theory techniques we explore the atomic and molecular correlations in this low-dimensional setting. We provide compelling evidence for an Ising deconfinement transition occurring between distinct superfluids and extract the Ising order parameter and correlation length of this unusual superfluid transition. This is supported by results for the entanglement entropy which reveal both the location of the transition and critical Ising degrees of freedom on the phase boundary.     

Absence of an Almeida-Thouless line in three-dimensional spin glasses

We present results of Monte Carlo simulations of the three-dimensional Edwards-Anderson Ising spin glass in the presence of a (random) field. A finite-size scaling analysis of the correlation length shows no indication of a transition, in contrast with the zero-field case. This suggests that there is no Almeida-Thouless line for short-range Ising spin glasses.     

Finite-size scaling approach for critical wetting: rationalization in terms of a bulk transition with an order parameter exponent equal to zero

Clarification of critical wetting with short-range forces by simulations has been hampered by the lack of accurate methods to locate where the transition occurs. We solve this problem by developing an anisotropic finite-size scaling approach and show that then the wetting transition is a "bulk" critical phenomenon with order parameter exponent equal to zero. For the Ising model in two dimensions, known exact results are straightforwardly reproduced. In three dimensions, it is shown that previous estimates for the location of the transition need revision, but the conclusions about a slow crossover away from mean-field behavior remain unaltered.     

Nonlinearity in cooperative systems-dynamical Bethe-Ising model

The dynamics of the short-range order as well as the long-range order in the nonlinear cooperative system is investigated specifically for a kinetic Ising model in the Bethe approximation. The phenomena of critical slowing down near the transition temperatureT _c and anomalous fluctuation belowT _c are directly related to the instability of the long-range order. The dynamics of the short-range order is essentially a fast mode and is noncritical. However, through the nonlinear coupling the short-range order is also influenced by the critical behavior of the long-range order.