http://cds.cern.ch/record/147992/files/198312192.pdf

Chiral perturbation theory to one loop

This is a tutorial review on the Potts model aimed at bringing out in an organized fashion the essential and important properties of the standard Potts model. Emphasis is placed on exact and rigorous results, but other aspects of the problem are also described to achieve a unified perspective. Topics reviewed include the mean-field theory, duality relations, series expansions, critical properties, experimental realizations, and the relationship of the Potts model with other lattice-statistical problems.

The Potts model

Feynman's 1982 conjecture, that quantum computers can be programmed to simulate any local quantum system, is shown to be correct.

https://science.sciencemag.org/content/sci/273/5278/1073.full.pdf

Universal Quantum Simulators

We propose an efficient Monte Carlo algorithm for simulating a “hardly-relaxing” system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replicas is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional ± J Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multi-canonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.

Exchange Monte Carlo Method and Application to Spin Glass Simulations

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new andpromising methods for the numerical solution of nonlinear partial differential equations. The bookprovides an introduction for graduate students and researchers. Working knowledge of calculus isrequired and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellularautomata are outlined in Chapter 2. The properties of various LGCA and special coding techniquesare discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessarytheoretical background for LGCA and LBM. The properties of lattice Boltzmann models and amethod for their construction are presented in Chapter 5.

/pdf/lattice-gas-cellular-automata-and-lattice-boltzmann-models-2kkc77jjx8.pdf

Lattice-Gas Cellular Automata and Lattice Boltzmann Models

Using Monte Carlo techniques, we evaluate the path integral for the four-dimensional lattice gauge theory with a Z/sub 2/ gauge group. The system exhibits a first-order transition. This is contrary to the implications of the approximate Migdal recursion relations but consistant with mean-field-theory arguments. Our ''data'' agree well with a low-temperature expansion and the exact duality between the high- and low-temperature phases.

Experiments with a Gauge-Invariant Ising System

Monte Carlo computations in lattice gauge theories

It is shown that in an SU(2) lattice gauge theory, in the approximation where internal quark closed loops are neglected, chiral symmetry is broken. With use of partially conserved axial-vector current f/sub ..pi../, the bare masses of the u and d quarks, and the rho and delta masses are estimated.

Computer estimates of meson masses in SU (2) lattice gauge theory

By means of a constrained variational calculation we determine the interaction energy of two-vortex configurations in the Ginzburg-Landau theory or, equivalently, in the Abelian Higgs model. The energy is evaluated as a function of the separation between vortices and of the parameter $\ensuremath{\lambda}$, which measures the relative strength of the matter self-coupling and the electromagnetic coupling. Our results provide a precise determination of the inter-vortex potential, attractive for $\ensuremath{\lambda}l1$ and repulsive for $\ensuremath{\lambda}g1$. They also show that for $\ensuremath{\lambda}=1$ the lower bound on the energy which can be then derived is actually reached at all separations and, therefore, that in this case vortices do not interact.

Interaction energy of superconducting vortices

Using Monte Carlo techniques, we study the thermodynamics of four-dimensional Euclidean lattice gauge theories, with gauge groups ${Z}_{N}$ and U(1). For $N\ensuremath{\le}4$ the models exhibit a single first-order phase transition, while for $N\ensuremath{\ge}5$ we observe two transitions of higher order. As $N$ increases, one of these transitions moves toward zero temperature, whereas the other remains at finite temperature and survives in the U(1) limit. The behavior of the Wilson loop factor is also analyzed for the ${Z}_{2}$ and ${Z}_{6}$ models.

Claudio Rebbi

Papers

Experiments with a Gauge-Invariant Ising System

Monte Carlo computations in lattice gauge theories

Computer estimates of meson masses in SU (2) lattice gauge theory

Interaction energy of superconducting vortices

Monte Carlo Study of Abelian Lattice Gauge Theories