Using Monte Carlo techniques, we evaluate path integrals for pure SU(2) gauge fields. Wilson's regularization procedure on a lattice of up to ${10}^{4}$ sites controls ultraviolet divergences. Our renormalization prescription, based confinement, is hold fixed the string tension, coefficient asymptotic linear potential between sources in fundamental representation group. Upon reducing cutoff, observe logarithmic decrease bare coupling constant manner consistent with perturbative...

A new algorithm for the simulation of statistical systems is presented. The procedure produces a random walk through configurations constant total energy. It computationally simple and applicable to both discrete continuous variables.

Using Monte Carlo techniques, we study pure SU(2) gauge fields in four and five space-time dimensions a compact SO(2) field dimensions. Ultraviolet divergences are regulated with Wilson's lattice prescription. Both show clear phase transitions between the confining regime at strong coupling spin-wave weak coupling. No change is seen for four-dimensional theory.

I study a simple variation of the algorithm Metropolis et al. for simulating statistical systems. The trial changes in any given variable are taken from region phase space far old value but involving only small energy. This results correlation times which short compared to usual applications Tests with SU(2) and SU(3) lattice gauge theories indicate substantial possible savings computation time relative standard approaches.

Using Monte Carlo methods with Wilson's lattice cutoff, the asymptotic-freedom scales of SU(2) and SU(3) gauge theories without quarks are calculated.Received 12 May 1980DOI:https://doi.org/10.1103/PhysRevLett.45.313©1980 American Physical Society

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

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

We present a simple recursive iteration of the leapfrog discretization Newton's equations which leads to removal finite-step-size error any desired order. This is done in manner that preserves phase-space areas and reversibility, as required for use hybrid Monte Carlo method simulating fermionic fields. The resulting asymptotic volume dependence exp[(lnV${)}^{1/2}$]. test scheme on (2+1)-dimensional Hubbard model.

We use the transfer-matrix formalism of statistical mechanics to relate Wilson's Lagrangian approach and Kogut-Susskind Hamiltonian gauge theories on a lattice. As preliminary we discuss fixing in theory. This process leaves invariant Green's functions singlet operators. Taking timelike lattice spacing zero, extract from transfer matrix ${A}_{0} = 0$.

We study a simple generalization of Wilson's SU(2) lattice gauge theory. In various limits the model reduces to usual SU(2), SO(3), or ${Z}_{2}$ models. Using Monte Carlo techniques on four-dimensional lattice, we follow known SO(3) and first-order transitions into phase diagram. They merge at triple point continue together critical end point. The peak in specific heat is shadow this nearby singularity.

A magnetic field applied to a cross-linked ladder compound can generate isolated electronic states bound the ends of chain. After exploring interference phenomena responsible, I discuss connection domain-wall approach chiral fermions in lattice gauge theory. The robust nature under small variations bond strengths is tied symmetry and multiplicative renormalization fermion masses.

I discuss algorithms for simulating many-fermion systems via global updatings of auxiliary fields followed by an accept-reject stage which eliminates finite-step-size errors. When the system size is larger than correlation length, these procedures should require computer time growing only slightly faster linearly with volume V. A corrected Langevin scheme asymptotically display a ${V}^{4/3}$ behavior, while hybrid Monte Carlo can behave as ${V}^{5/4}$. present some tests latter algorithm on...

We give a graphical algorithm for evaluation of invariant integrals polynomials in SU(N) group elements. Such occur strongly coupled lattice gauge theory. The results are expressed terms totally antisymmetric tensors and Kronecker delta symbols.

We present Monte Carlo studies of $Z(N)$ and U(1) lattice gauge theories in three space-time dimensions. The theory is analyzed via its dual spin system. find that has one phase transition moves to zero temperature as $N\ensuremath{\rightarrow}\ensuremath{\infty}$. only a single, confining phase. A study Wilson loops $Z(8)$ shows the coefficient area law vanishes for all temperatures below critical temperature. No such seen string tension theory. also five dimensions see clear signal...

I present Monte Carlo evidence for a first-order phase transition in pure SU(5) lattice gauge theory with Wilson's action four space-time dimensions. Although less clear, similar is strongly suggested already SU(4).

We investigate the contribution of a pole at $\ensuremath{\alpha}=0$ to forward Compton scattering using finite-energy sum rules. conclude that an experiment measuring total photoabsorption cross section from \ensuremath{\sim}1 10-15 BeV with accuracy 5% will detect such whose magnitude is larger than 30% Thomson limit.

This article is a pedagogical exploration of the nonperturbative issues entwining lattice gauge theory, anomalies, and chiral symmetry. After briefly reviewing importance symmetry in particle physics, author discusses how anomalies complicate formulations. Considerable information can be deduced from effective Lagrangians, helping interpret expectations for models elucidating role CP-violating parameter \ensuremath{\Theta}. One particularly elegant scheme exploring this physics on presented...