Study of a microcanonical algorithm on the ±J\pm J spin glass model in d=3

We consider a microcanonical local algorithm to be applied on the $\pm J$ spin glass model. We have compared the results coming from a microcanonical Monte Carlo simulation with those from a canonical one: Thermalization times, spin glass susceptibilities and Binder parameters. For a fixed lattice size we found different results between the two thermodynamic ensembles, which tend to vanish at bigger volumes. Moreover, microcanonical thermalization times are longer than the canonical ones. Finally we have checked that one of the Guerra relations is satisfied with good precision for the two largest lattices.Comment: Revised version. Latex 14 pages, 6 figures. To be published in Comput. Phys. Commu

Monte-Carlo simulation of supercooled liquids using a self-consistent local temperature

We combine Creutz energy conservation with Kawasaki spin exchange to simulate the microcanonical dynamics of a system of interacting particles. Relaxation occurs via Glauber spin-flip activation using a self-consistent temperature. Heterogeneity in the dynamics comes from finite-size constraints on the spin exchange that yield a distribution of correlated regions. The simulation produces a high-frequency response that can be identified with the boson peak, and a lower-frequency peak that contains non-Debye relaxation and non-Arrhenius activation, similar to the primary response of supercooled liquids.Comment: 16 pages, 4 figure

A new approach to the study of the ground-state properties of 2D Ising spin glass

A new approach known as flat histogram method is used to study the +/-J Ising spin glass in two dimensions. Temperature dependence of the energy, the entropy, and other physical quantities can be easily calculated and we give the results for the zero-temperature limit. For the ground-state energy and entropy of an infinite system size, we estimate e0 = -1.4007 +/- 0.0085 and s0 = 0.0709 +/- 0.006, respectively. Both of them agree well with previous calculations. The time to find the ground-states as well as the tunneling times of the algorithm are also reported and compared with other methods.Comment: 11 pages, 4 figure

SUE: A Special Purpose Computer for Spin Glass Models

The use of last generation Programmable Electronic Components makes possible the construction of very powerful and competitive special purpose computers. We have designed, constructed and tested a three-dimensional Spin Glass model dedicated machine, which consists of 12 identical boards. Each single board can simulate 8 different systems, updating all the systems at every clock cycle. The update speed of the whole machine is 217ps/spin with 48 MHz clock frequency. A device devoted to fast random number generation has been developed and included in every board. The on-board reprogrammability permits us to change easily the lattice size, or even the update algorithm or the action. We present here a detailed description of the machine and the first runs using the Heat Bath algorithm.Comment: Submitted to Computer Physics Communications, 19 pages, 5 figures, references adde

Static and Dynamic Critical Behavior of a Symmetrical Binary Fluid: A Computer Simulation

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grandcanonical Monte Carlo (SGMC) and Molecular Dynamics (MD) methods near a liquid-liquid critical temperature $T_c$. Choosing equal chemical potentials for the two species, the SGMC switches identities (${\rm A} \to {\rm B} \to {\rm A}$) to generate well-equilibrated configurations of the system on the coexistence curve for $T<T_c$ and at the critical concentration, $x_c=1/2$, for $T>T_c$. A finite-size scaling analysis of the concentration susceptibility above $T_c$ and of the order parameter below $T_c$ is performed, varying the number of particles from N=400 to 12800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.Comment: 35 pages, 13 figure

Density-of-states of many-body quantum systems from tensor networks

We present a technique to compute the microcanonical thermodynamical properties of a manybody quantum system using tensor networks. The Density Of States (DOS), and more general spectral properties, are evaluated by means of a Hubbard-Stratonovich transformation performed on top of a real-time evolution, which is carried out via numerical methods based on tensor networks. As a consequence, the free energy and thermal averages can be also calculated. We test this approach on the one-dimensional Ising and Fermi-Hubbard models. Using matrix product states, we show that the thermodynamical quantities as a function of temperature are in very good agreement with the exact results. This approach can be extended to higher-dimensional system by properly employing other types of tensor networks.Comment: 8 pages, 7 figure

The Big World of Nanothermodynamics

Nanothermodynamics extends standard thermodynamics to facilitate finite-size effects on the scale of nanometers. A key ingredient is Hill's subdivision potential that accommodates the non-extensive energy of independent small systems, similar to how Gibbs' chemical potential accommodates distinct particles. Nanothermodynamics is essential for characterizing the thermal equilibrium distribution of independently relaxing regions inside bulk samples, as is found for the primary response of most materials using various experimental techniques. The subdivision potential ensures strict adherence to the laws of thermodynamics: total energy is conserved by including an instantaneous contribution from the entropy of local configurations, and total entropy remains maximized by coupling to a thermal bath. A unique feature of nanothermodynamics is the completely-open nanocanonical ensemble. Another feature is that particles within each region become statistically indistinguishable, which avoids non-extensive entropy, and mimics quantum-mechanical behavior. Applied to mean-field theory, nanothermodynamics gives a heterogeneous distribution of regions that yields stretched-exponential relaxation and super-Arrhenius activation. Applied to Monte Carlo simulations, there is a nonlinear correction to Boltzmann's factor that improves agreement between the Ising model and measured non-classical critical scaling in magnetic materials. Nanothermodynamics also provides a fundamental mechanism for the 1/f noise found in many materials.Comment: 22 pages, 14 figures, revie