Scaling laws for the 2d 8-state Potts model with Fixed Boundary Conditions

We study the effects of frozen boundaries in a Monte Carlo simulation near a first order phase transition. Recent theoretical analysis of the dynamics of first order phase transitions has enabled to state the scaling laws governing the critical regime of the transition. We check these new scaling laws performing a Monte Carlo simulation of the 2d, 8-state spin Potts model. In particular, our results support a pseudo-critical beta finite-size scaling of the form beta(infinity) + a/L + b/L^2, instead of beta(infinity) + c/L^d + d/L^{2d}. Moreover, our value for the latent heat is 0.294(11), which does not coincide with the latent heat analytically derived for the same model if periodic boundary conditions are assumed, which is 0.486358...Comment: 10 pages, 3 postscript figure

Surface critical exponents at a uniaxial Lifshitz point

Using Monte Carlo techniques, the surface critical behaviour of three-dimensional semi-infinite ANNNI models with different surface orientations with respect to the axis of competing interactions is investigated. Special attention is thereby paid to the surface criticality at the bulk uniaxial Lifshitz point encountered in this model. The presented Monte Carlo results show that the mean-field description of semi-infinite ANNNI models is qualitatively correct. Lifshitz point surface critical exponents at the ordinary transition are found to depend on the surface orientation. At the special transition point, however, no clear dependency of the critical exponents on the surface orientation is revealed. The values of the surface critical exponents presented in this study are the first estimates available beyond mean-field theory.Comment: 10 pages, 7 figures include

Kinetics in one-dimensional lattice gas and Ising models from time-dependent density functional theory

Time-dependent density functional theory, proposed recently in the context of atomic diffusion and non-equilibrium processes in solids, is tested against Monte Carlo simulation. In order to assess the basic approximation of that theory, the representation of non-equilibrium states by a local equilibrium distribution function, we focus on one-dimensional lattice models, where all equilibrium properties can be worked exactly from the known free energy as a functional of the density. This functional determines the thermodynamic driving forces away from equilibrium. In our studies of the interfacial kinetics of atomic hopping and spin relaxation, we find excellent agreement with simulations, suggesting that the method is useful also for treating more complex problems.Comment: 8 pages, 5 figures, submitted to Phys. Rev.

Reexamination of the long-range Potts model: a multicanonical approach

We investigate the critical behavior of the one-dimensional q-state Potts model with long-range (LR) interaction $1/r^{d+\sigma}$, using a multicanonical algorithm. The recursion scheme initially proposed by Berg is improved so as to make it suitable for a large class of LR models with unequally spaced energy levels. The choice of an efficient predictor and a reliable convergence criterion is discussed. We obtain transition temperatures in the first-order regime which are in far better agreement with mean-field predictions than in previous Monte Carlo studies. By relying on the location of spinodal points and resorting to scaling arguments, we determine the threshold value $\sigma_c(q)$ separating the first- and second-order regimes to two-digit precision within the range $3 \leq q \leq 9$. We offer convincing numerical evidence supporting $\sigma_c(q)Comment: 18 pages, 18 figure

Ordering and Demixing Transitions in Multicomponent Widom-Rowlinson Models

We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M between two and six there is a direct transition from the gas phase at z < z_d (M) to a demixed phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e. spatial symmetry but not particle symmetry is broken. The transition at z_d(M) appears to be first order for M \geq 5 putting it in the Potts model universality class. For large M the transition between the crystalline and demixed phase at z_d(M) can be proven to be first order with z_d(M) \sim M-2 + 1/M + ..., while z_c(M) is argued to behave as \mu_{cr}/M, with \mu_{cr} the value of the fugacity at which the one component hard square lattice gas has a transition, and to be always of the Ising type. Explicit calculations for the Bethe lattice with the coordination number q=4 give results similar to those for the square lattice except that the transition at z_d(M) becomes first order at M>2. This happens for all q, consistent with the model being in the Potts universality class.Comment: 26 pages, 15 postscript figure

Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems

The distributions $P(X)$ of singular thermodynamic quantities in an ensemble of quenched random samples of linear size $l$ at the critical point $T_c$ are studied by Monte Carlo in two models. Our results confirm predictions of Aharony and Harris based on Renormalization group considerations. For an Ashkin-Teller model with strong but irrelevant bond randomness we find that the relative squared width, $R_X$, of $P(X)$ is weakly self averaging. $R_X\sim l^{\alpha/\nu}$, where $\alpha$ is the specific heat exponent and $\nu$ is the correlation length exponent of the pure model fixed point governing the transition. For the site dilute Ising model on a cubic lattice, known to be governed by a random fixed point, we find that $R_X$ tends to a universal constant independent of the amount of dilution (no self averaging). However this constant is different for canonical and grand canonical disorder. We study the distribution of the pseudo-critical temperatures $T_c(i,l)$ of the ensemble defined as the temperatures of the maximum susceptibility of each sample. We find that its variance scales as $(\delta T_c(l))^2 \sim l^{-2/\nu}$ and NOT as $\sim l^{-d}. We find that$R_\chi$is reduced by a factor of$\sim 70$with respect to$R_\chi (T_c)$by measuring$\chi$of each sample at$T_c(i,l)$. We analyze correlations between the magnetization at criticality$m_i(T_c,l)$and the pseudo-critical temperature$T_c(i,l)$in terms of a sample independent finite size scaling function of a sample dependent reduced temperature$(T-T_c(i,l))/T_c$. This function is found to be universal and to behave similarly to pure systems.Comment: 31 pages, 17 figures, submitted to Phys. Rev.

Computational Nuclear Physics and Post Hartree-Fock Methods

We present a computational approach to infinite nuclear matter employing Hartree-Fock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of chapters 9, 10 and 11 and serve as input for the correlation functions employed in Monte Carlo calculations in chapter 9, the in-medium similarity renormalization group theory of dense fermionic systems of chapter 10 and the Green's function approach in chapter 11. We provide extensive code examples and benchmark calculations, allowing thereby an eventual reader to start writing her/his own codes. We start with an object-oriented serial code and end with discussions on strategies for porting the code to present and planned high-performance computing facilities.Comment: 82 pages, to appear in Lecture Notes in Physics (Springer), "An advanced course in computational nuclear physics: Bridging the scales from quarks to neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editor

Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations

We investigate how the dynamics of a single chain influences the kinetics of early stage phase separation in a symmetric binary polymer mixture. We consider quenches from the disordered phase into the region of spinodal instability. On a mean field level we approach this problem with two methods: a dynamical extension of the self consistent field theory for Gaussian chains, with the density variables evolving in time, and the method of the external potential dynamics where the effective external fields are propagated in time. Different wave vector dependencies of the kinetic coefficient are taken into account. These early stages of spinodal decomposition are also studied through Monte Carlo simulations employing the bond fluctuation model that maps the chains -- in our case with 64 effective segments -- on a coarse grained lattice. The results obtained through self consistent field calculations and Monte Carlo simulations can be compared because the time, length, and temperature scales are mapped onto each other through the diffusion constant, the chain extension, and the energy of mixing. The quantitative comparison of the relaxation rate of the global structure factor shows that a kinetic coefficient according to the Rouse model gives a much better agreement than a local, i.e. wave vector independent, kinetic factor. Including fluctuations in the self consistent field calculations leads to a shorter time span of spinodal behaviour and a reduction of the relaxation rate for smaller wave vectors and prevents the relaxation rate from becoming negative for larger values of the wave vector. This is also in agreement with the simulation results.Comment: Phys.Rev.E in prin

Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states

When the two-dimensional random-bond Ising model is represented as a noninteracting fermion problem, it has the same symmetries as an ensemble of random matrices known as class D. A nonlinear sigma model analysis of the latter in two dimensions has previously led to the prediction of a metallic phase, in which the fermion eigenstates at zero energy are extended. In this paper we argue that such behavior cannot occur in the random-bond Ising model, by showing that the Ising spin correlations in the metallic phase violate the bound on such correlations that results from the reality of the Ising couplings. Some types of disorder in spinless or spin-polarized p-wave superconductors and paired fractional quantum Hall states allow a mapping onto an Ising model with real but correlated bonds, and hence a metallic phase is not possible there either. It is further argued that vortex disorder, which is generic in the fractional quantum Hall applications, destroys the ordered or weak-pairing phase, in which nonabelian statistics is obtained in the pure case.Comment: 13 pages; largely independent of cond-mat/0007254; V. 2: as publishe

Lattice-switch Monte Carlo

We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate configuration of the other by `switching' one set of lattice vectors for the other, while keeping the displacements with respect to the lattice sites constant. The sampling of the displacement configurations is biased, multicanonically, to favor paths leading to `gateway' arrangements for which the Monte Carlo switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. We explore and exploit the method in the context of extensive studies of systems of hard spheres. We show that the efficiency of the method is controlled by the extent to which the switch conserves correlated microstructure. We also show how, microscopically, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the differences between the free energies of the two close packed structures (fcc and hcp) in both the constant density and the constant pressure ensembles.Comment: 34 pages, 9 figures, RevTeX. To appear in Phys. Rev.