0000000000146693
AUTHOR
J. D. Reger
Diluted Heisenberg Ferromagnets with Competing Ferro- and Antiferromagnetic Interactions: Evidence for a New Universality Class?
The site-diluted classical face-centered cubic (fee) Heisenberg model with exchange between nearest and (J nn > 0) next nearest (J nnn =-J nn /2) neighbors is studied by Monte Carlo simulations using the heatbath algorithm in conjunction with histogram reweighting techniques. Finite size scaling analysis suggests that the diluted system crosses over to a new type of critical behavior, different from that of the pure system, in contrast to the prediction of the Harris criterion. But this model possibly can explain related experimental findings in Eu x Sr 1-x S.
Critical behavior of short range Potts glasses
We study by means of Monte Carlo simulations and the numerical transfer matrix technique the critical behavior of the short rangep=3 state Potts glass model in dimensionsd=2,3,4 with both Gaussian and bimodal (±J) nearest neighbor interactions on hypercubic lattices employing finite size scaling ideas. Ind=2 in addition the degeneracy of the glass ground state is computed as a function of the number of Potts states forp=3, 4, 5 and compared to that of the antiferromagnetic ground state. Our data indicate a transition into a glass phase atT=0 ind=2 with an algebraic singularity, aT=0 transition ind=3 with an essential singularity of the form χ∼exp(const.T−2), and an algebraic singularity atT…
Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution
We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicL d geometry,L being the linear dimension of the system, and surface effects are avoided by periodic boundary conditions. We assume that upon lowering the temperature the system discontinuously goes to one ofq ordered states, such as it e.g. happens for the Potts model ind=3 forq≧3, with the correlation length ξ of order parameter fluctuation staying finite at the transition. We then describe each of theseq ordered phases and the disordered phase forL≫ξ by a properly weighted Gaussian. From this phenomenological ansatz for the total distribution of the order parameter, all moments of interest…
Monte Carlo study of the order-parameter distribution in the four-dimensional Ising spin glass
We investigate the order-parameter distribution P(q) of the Ising spin glass with nearest-neighbor interactions in four dimensions using Monte Carlo simulations on lattices of linear dimension up to L=6. We find that, below the transition temperature ${\mathit{T}}_{\mathit{c}}$, the weight at small q seems to saturate to a nonzero value as the size increases, similar to the infinite-range Sherrington-Kirkpatrick model. We discuss our results in the light of recent theoretical predictions for the nature of the spin-glass phase.
Finite-Size Scaling Study of the Simple Cubic Three-State Potts Glass
During the last few years the Potts glass model has attracted more and more attention. It is considered as a first step towards modelling the phase transition of structural and orientational glasses. A mean-field approach /1/ predicts a low temperature behavior completely different from what is known from Ising spin glasses /2/. But short range models differ markedly from mean-field-predictions. So it is natural to ask, how the short range Potts glass behaves. Especially the question of the lower critical dimension d l is important, below which a finite temperature transition ceases to occur. We tried to answer this by combining Monte-Carlo simulations with a finite-size scaling analysis. T…
Monte Carlo study of the bimodal three-state Potts glass
Employing Monte Carlo simulations, we compute the spin-glass susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{SG}}$(T) of the three-state Potts glass model on a simple-cubic lattice for various temperatures and lattice sizes ranging from L=4 to 10. We use the discrete \ifmmode\pm\else\textpm\fi{}J distribution for the bonds. Comparing our results with a recent high-temperature series expansion, we find a systematic deviation at lower temperatures, which cannot be explained by finite-size effects in our data. The low-temperature behavior of ${\mathrm{\ensuremath{\chi}}}_{\mathrm{SG}}$(T) is compatible with d = 3 being the lower critical dimension of this model.
Quantum Monte Carlo Simulations of Models Related to High-Tc Superconductivity on a Transputer Network
Much of the insight into the low temperature behaviour of two-dimensional quantum antiferromagnets has been recently obtained by extensive Monte Carlo. These models are relevant in the study of the magnetic behaviour of high Tc compounds containing copper-oxide layers. While of little technical importance, the physical properties of these models are certainly important for the understanding of the new type of behaviour that leads to superconductivity under certain conditions.
Finite-size-scaling study of the simple cubic three-state Potts glass: Possible lower critical dimension d=3.
For small lattices with linear dimension L ranging from L=3 to L=8 we obtain the distribution function P(q) of the overlap q between two real replicas of the three-state Potts-glass model with symmetric nearest-neighbor interaction with a Gaussian distribution. A finite-size-scaling analysis suggests a zero-temperature transition to occur with an exponentially diverging correlation length ${\ensuremath{\xi}}_{\mathrm{SG}}$\ensuremath{\sim}exp(C/${\mathit{T}}^{\mathrm{\ensuremath{\sigma}}}$). This implies that d=3 is the lower critical dimension.
MONTE CARLO METHODS FOR FIRST ORDER PHASE TRANSITIONS: SOME RECENT PROGRESS
This brief review discusses methods to locate and characterize first order phase transitions, paying particular attention to finite size effects. In the first part, the order parameter probability distribution and its fourth-order cumulant is discussed for thermally driven first-order transitions (the 3-state Potts model in d=3 dimensions is treated as an example). First-order transitions are characterized by a minimum of the cumulant, which gets very deep for large enough systems. In the second part, we discuss how to locate first order phase boundaries ending in a critical point in a large parameter space. As an example, the study of the unmixing transition of asymmetric polymer mixtures…
The Gauge Glass Transition
Results of Monte Carlo simulations in three and four spatial dimensions of a simple model that seems to have the necessary ingredients for disordered type-II superconductor behavior in an external magnetic field are reported. The data suggest that in d = 3 dimensions there is a finite temperature phase transition at T ≈ 0.45 into a truly superconducting vortex glass phase with infinite d.c. conductivity The (effective) correlation length exponent v and the dynamic critical exponent z at this transition are in good agreement with experiments. In d = 4 dimensions the gauge glass transition is located at T ≈ 0.95. It is concluded that the lack of time reversal symmetry in the model places it i…
High-temperature series expansion for the relaxation times of the two dimensional Ising model
We derive the high temperature series expansions for the two relaxation times of the single spin-flip kinetic Ising model on the square lattice. The series for the linear relaxation time τl is obtained with 20 non-trivial terms, and the analysis yields 2.183±0.005 as the value of the critical exponentΔl, which is equal to the dynamical critical exponentz in the two-dimensional case. For the non-linear relaxation time we obtain 15 non-trivial terms, and the analysis leads to the resultsΔnl = 2.08 ± 0.07. The scaling relationΔl −Δnl = β (β being the exponent of the order parameter) seems to be fulfilled, though the error bars ofΔnl are still quite substantial. In addition, we obtain the serie…
Theory of orientational glasses models, concepts, simulations
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…
Dynamics of Ising spin glasses far below the lower critical dimension: The one-dimensional case and small clusters
The Glauber model is studied for symmetric distributions (±J and gaussian) of the nearest-neighbour interactionJ, including a magnetic field. For small clusters of spins (closed rings ofN bonds, withN≦7) the complex magnetic susceptibility χ(ω) and the time-dependent remanent magnetizationm(t) are found exactly for given bond configurations {Jij} by diagonalization of the Liouville operator; apart from the ±J model, the average over {Jij} must be done numerically by simple random sampling Monte Carlo. Nevertheless our accuracy is much better than corresponding dynamic Monte Carlo simulations, even if one considers the extrapolation toN→∞.
Vortex-glass transition in three dimensions.
We investigate the possibility of a vortex-glass transition in a disordered type-II superconductor in a magnetic field in three dimensions by numerical studies of a simplified model. Monte Carlo simulations at finite temperature and domain-wall renormalization-group calculations at {ital T}=0 indicate that {ital d}=3 is just above the lower critical dimension {ital d}{sub {ital l}}, though the possibility that {ital d}{sub {ital l}}=3 cannot be definitely ruled out. A comparison is made with {ital XY} and Ising spin glasses. The (effective) correlation-length exponent {nu} and dynamical exponent {ital z} are in fairly good agreement with experiment.
The Ground State of the 2-Dimensional Potts Glass
We study the ground state of the 3-state Potts glass in 2 dimensions with a Gaussian distribution of couplings by domain wall renormalization group techniques. We find that the glass correlation function decays to a finite value within a distance of about 2.4 lattice spacings. Thus, there is long-range order in the ground state even though, as found earlier, there is a finite zero-point entropy.
The four dimensional Ising spin glass: A Monte Carlo study (invited)
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.