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

Lower Critical Dimension of Ising Spin Glasses

Exact ground states of two-dimensional Ising spin glasses with Gaussian and bimodal (+- J) distributions of the disorder are calculated using a ``matching'' algorithm, which allows large system sizes of up to N=480^2 spins to be investigated. We study domain walls induced by two rather different types of boundary-condition changes, and, in each case, analyze the system-size dependence of an appropriately defined ``defect energy'', which we denote by DE. For Gaussian disorder, we find a power-law behavior DE ~ L^\theta, with \theta=-0.266(2) and \theta=-0.282(2) for the two types of boundary condition changes. These results are in reasonable agreement with each other, allowing for small systematic effects. They also agree well with earlier work on smaller sizes. The negative value indicates that two dimensions is below the lower critical dimension d_c. For the +-J model, we obtain a different result, namely the domain-wall energy saturates at a nonzero value for L\to \infty, so \theta = 0, indicating that the lower critical dimension for the +-J model exactly d_c=2.Comment: 4 pages, 4 figures, 1 table, revte

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

Cosmological model with interactions in the dark sector

A cosmological model is proposed for the current Universe consisted of non-interacting baryonic matter and interacting dark components. The dark energy and dark matter are coupled through their effective barotropic indexes, which are considered as functions of the ratio between their energy densities. It is investigated two cases where the ratio is asymptotically stable and their parameters are adjusted by considering best fits to Hubble function data. It is shown that the deceleration parameter, the densities parameters, and the luminosity distance have the correct behavior which is expected for a viable present scenario of the Universe.Comment: 6 pages, 8 figure

No spin-glass transition in the "mobile-bond" model

The recently introduced ``mobile-bond'' model for two-dimensional spin glasses is studied. The model is characterized by an annealing temperature T_q. On the basis of Monte Carlo simulations of small systems it has been claimed that this model exhibits a non-trivial spin-glass transition at finite temperature for small values of T_q. Here the model is studied by means of exact ground-state calculations of large systems up to N=256^2. The scaling of domain-wall energies is investigated as a function of the system size. For small values T_q<0.95 the system behaves like a (gauge-transformed) ferromagnet having a small fraction of frustrated plaquettes. For T_q>=0.95 the system behaves like the standard two-dimensional +-J spin-glass, i.e. it does NOT exhibit a phase transition at T>0.Comment: 4 pages, 5 figures, RevTe

The Percolation Signature of the Spin Glass Transition

Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering -- both in short-range (EA) and infinite-range (SK) models -- within a two-replica FK representation and also within the different Chayes-Machta-Redner two-replica graphical representation. Based on numerical studies of the $\pm J$ EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of {\it two} percolating clusters of {\it unequal} densities.Comment: 13 pages, 6 figure

The phase diagram of quantum systems: Heisenberg antiferromagnets

A novel approach for studying phase transitions in systems with quantum degrees of freedom is discussed. Starting from the microscopic hamiltonian of a quantum model, we first derive a set of exact differential equations for the free energy and the correlation functions describing the effects of fluctuations on the thermodynamics of the system. These equations reproduce the full renormalization group structure in the neighborhood of a critical point keeping, at the same time, full information on the non universal properties of the model. As a concrete application we investigate the phase diagram of a Heisenberg antiferromagnet in a staggered external magnetic field. At long wavelengths the known relationship to the Quantum Non Linear Sigma Model naturally emerges from our approach. By representing the two point function in an approximate analytical form, we obtain a closed partial differential equation which is then solved numerically. The results in three dimensions are in good agreement with available Quantum Monte Carlo simulations and series expansions. More refined approximations to the general framework presented here and few applications to other models are briefly discussed.Comment: 17 pages, 7 figure

Generating droplets in two-dimensional Ising spin glasses by using matching algorithms

We study the behavior of droplets for two dimensional Ising spin glasses with Gaussian interactions. We use an exact matching algorithm which enables study of systems with linear dimension L up to 240, which is larger than is possible with other approaches. But the method only allows certain classes of droplets to be generated. We study single-bond, cross and a category of fixed volume droplets as well as first excitations. By comparison with similar or equivalent droplets generated in previous works, the advantages but also the limitations of this approach are revealed. In particular we have studied the scaling behavior of the droplet energies and droplet sizes. In most cases, a crossover of the data can be observed such that for large sizes the behavior is compatible with the one-exponent scenario of the droplet theory. Only for the case of first excitations, no clear conclusion can be reached, probably because even with the matching approach the accessible system sizes are still too small.Comment: 11 pages, 16 figures, revte

Exchange anisotropy, disorder and frustration in diluted, predominantly ferromagnetic, Heisenberg spin systems

Motivated by the recent suggestion of anisotropic effective exchange interactions between Mn spins in Ga$_{1-x}$Mn$_x$As (arising as a result of spin-orbit coupling), we study their effects in diluted Heisenberg spin systems. We perform Monte Carlo simulations on several phenomenological model spin Hamiltonians, and investigate the extent to which frustration induced by anisotropic exchanges can reduce the low temperature magnetization in these models and the interplay of this effect with disorder in the exchange. In a model with low coordination number and purely ferromagnetic (FM) exchanges, we find that the low temperature magnetization is gradually reduced as exchange anisotropy is turned on. However, as the connectivity of the model is increased, the effect of small-to-moderate anisotropy is suppressed, and the magnetization regains its maximum saturation value at low temperatures unless the distribution of exchanges is very wide. To obtain significant suppression of the low temperature magnetization in a model with high connectivity, as is found for long-range interactions, we find it necessary to have both ferromagnetic and antiferromagnetic (AFM) exchanges (e.g. as in the RKKY interaction). This implies that disorder in the sign of the exchange interaction is much more effective in suppressing magnetization at low temperatures than exchange anisotropy.Comment: 9 pages, 8 figure

Metastable States in Spin Glasses and Disordered Ferromagnets

We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical and is based on the convergence of a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit. The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations and relations to thermodynamic states. For example, we show that their overlap distribution is a delta-function at zero. We also define a dynamics for M=infinity, which provides a potential tool for investigating ground state structure.Comment: 34 pages (LaTeX); to appear in Physical Review