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Register a new userConfigurations and Observables in an Ising Model with Heat Flow
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We study a two dimensional Ising model between thermostats at different temperatures. By applying the recently introduced KQ dynamics, we show that the system reaches a steady state with coexisting phases transversal to the heat flow. The relevance of such complex states on thermodynamic or geometrical observables is investigated. In particular, we study energy, magnetization and metric properties of interfaces and clusters which, in principle, are sensitive to local features of configurations. With respect to equilibrium states, the presence of the heat flow amplifies the fluctuations of both thermodynamic and geometrical observables in a domain around the critical energy. The dependence of this phenomenon on various parameters (size, thermal gradient, interaction) is discussed also with reference to other possible diffusive models.
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In this paper, we use the dimer method to obtain the free energy of Ising models consisting of repeated horizontal strips of width $m$ connected by sequences of vertical strings of length $n$ mutually separated by distance $N$, with $N$ arbitrary, to investigate the effects of connectivity and proximity on the specific heat. The decoration method is used to transform the strings of $n+1$ spins interacting with their nearest neighbors with coupling $J$ into a pair with coupling $bar J$ between the two spins. The free energy per site is given as a single integral and some results for critical temperatures are derived.
We study the dynamical behavior of a square lattice Ising model with exchange and dipolar interactions by means of Monte Carlo simulations. After a sudden quench to low temperatures we find that the system may undergo a coarsening process where stripe phases with different orientations compete or alternatively it can relax initially to a metastable nematic phase and then decay to the equilibrium stripe phase through nucleation. We measure the distribution of equilibration times for both processes and compute their relative probability of occurrence as a function of temperature and system size. This peculiar relaxation mechanism is due to the strong metastability of the nematic phase, which goes deep in the low temperature stripe phase. We also measure quasi-equilibrium autocorrelations in a wide range of temperatures. They show a distinct decay to a plateau that we identify as due to a finite fraction of frozen spins in the nematic phase. We find indications that the plateau is a finite size effect. Relaxation times as a function of temperature in the metastable region show super-Arrhenius behavior, suggesting a possible glassy behavior of the system at low temperatures.
The bond-propagation (BP) algorithm for the specific heat of the two dimensional Ising model is developed and that for the internal energy is completed. Using these algorithms, we study the critical internal energy and specific heat of the model on the square lattice and triangular lattice with free boundaries. Comparing with previous works [X.-T. Wu {it et al} Phys. Rev. E {bf 86}, 041149 (2012) and Phys. Rev. E {bf 87}, 022124 (2013)], we reach much higher accuracy ($10^{-26}$) of the internal energy and specific heat, compared to the accuracy $10^{-11}$ of the internal energy and $10^{-9}$ of the specific heat reached in the previous works. This leads to much more accurate estimations of the edge and corner terms. The exact values of some edge and corner terms are therefore conjectured. The accurate forms of finite-size scaling for the internal energy and specific heat are determined for the rectangle-shaped square lattice with various aspect ratios and various shaped triangular lattice. For the rectangle-shaped square and triangular lattices and the triangle-shaped triangular lattice, there is no logarithmic correction terms of order higher than 1/S, with S the area of the system. For the triangular lattice in rhombus, trapezoid and hexagonal shapes, there exist logarithmic correction terms of order higher than 1/S for the internal energy, and logarithmic correction terms of all orders for the specific heat.
Statistical mechanical models with local interactions in $d>1$ dimension can be regarded as $d=1$ dimensional models with regular long range interactions. In this paper we study the critical properties of Ising models having $V$ sites, each having $z$ randomly chosen neighbors. For $z=2$ the model reduces to the $d=1$ Ising model. For $z= infty$ we get a mean field model. We find that for finite $z > 2$ the system has a second order phase transition characterized by a length scale $L={rm ln}V$ and mean field critical exponents that are independent of $z$.
A framework for studying the effect of the coupling to the heat bath in models exhibiting anomalous heat conduction is described. The framework is applied to the harmonic chain with momentum exchange model where the non-trivial temperature profile is calculated. In this approach one first uses the hydrodynamic (HD) equations to calculate the equilibrium current-current correlation function in large but finite chains, explicitly taking into account the BCs resulting from the coupling to the heat reservoirs. Making use of a linear response relation, the anomalous conductivity exponent $alpha$ and an integral equation for the temperature profile are obtained. The temperature profile is found to be singular at the boundaries with an exponent which varies continuously with the coupling to the heat reservoirs expressed by the BCs. In addition, the relation between the harmonic chain and a system of noninteracting L{e}vy walkers is made explicit, where different BCs of the chain correspond to different reflection coefficients of the L{e}vy particles.
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