Topology and θ\theta dependence in finite temperature G2G_2 lattice gauge theory

In this work we study the topological properties of the $G_2$ lattice gauge theory by means of Monte Carlo simulations. We focus on the behaviour of topological quantities across the deconfinement transition and investigate observables related to the $\theta$ dependence of the free energy. As in $SU(N)$ gauge theories, an abrupt change happens at deconfinement and an instanton gas behaviour rapidly sets in for $T>T_c$.Comment: 11 pages, 8 eps figures (typos corrected in eq.2.5 and 2.7 with respect to the published version

The topological properties of QCD at high temperature: problems and perspectives

Lattice computations are the only first principle method capable of quantitatively assessing the topological properties of QCD at high temperature, however the numerical determination of the topological properties of QCD, especially in the high temperature phase, is a notoriously difficult problem. We will discuss the difficulties encountered in such a computation and some strategies that have been proposed to avoid (or at least to alleviate) them.Comment: 12 pages, 5 eps figs. Talk given at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada (Spain

The Peierls argument for higher dimensional Ising models

The Peierls argument is a mathematically rigorous and intuitive method to show the presence of a non-vanishing spontaneous magnetization in some lattice models. This argument is typically explained for the $D=2$ Ising model in a way which cannot be easily generalized to higher dimension. The aim of this paper is to present an elementary discussion of the Peierls argument for the general $D$-dimensional Ising model.Comment: 14 pages, 5 eps figures, minor change

Conservation and specialization in PAS domain dynamics

The PAS (Per-ARNT-Sim) superfamily is presented as a well-suited study case to demonstrate how comparison of functional motions among distant homologous proteins with conserved fold characteristics may give insight into their functional specialization. Based on the importance of structural flexibility of the receptive structures in anticipating the signal-induced conformational changes of these sensory systems, the dynamics of these structures were analysed. Molecular dynamics was proved to be an effective method to obtain a reliable picture of the dynamics of the crystal structures of HERG, phy3, PYP and FixL, provided that an extensive conformational space sampling is performed. Other reliable sources of dynamic information were the ensembles of NMR structures of hPASK, HIF-2α and PYP. Essential dynamics analysis was successfully employed to extract the relevant information from the sampled conformational spaces. Comparison of motion patterns in the essential subspaces, based on the structural alignment, allowed identification of the specialized region in each domain. This appears to be evolved in the superfamily by following a specific trend, that also suggests the presence of a limited number of general solutions adopted by the PAS domains to sense external signals. These findings may give insight into unknown mechanisms of PAS domains and guide further experimental studies. © The Author 2005. Published by Oxford University Press. All rights reserved

Color flux tubes in SU(3)SU(3) Yang-Mills theory: an investigation with the connected correlator

In this work we perform an investigation of the flux tube between two static color sources in four dimensional $SU(3)$ Yang-Mills theory, using the so called connected correlator. Contrary to most previous studies we do not use any smoothing algorithm to facilitate the evaluation of the correlator, that is performed using only stochastically exact techniques. We first examine the renormalization properties of the connected operator, then we present our numerical data for the longitudinal chromoelectric component of the flux tube, that are used to extract the dual superconductivity parameters.Comment: 8 pages, 6 eps figure

The topological susceptibility of two-dimensional U(N)U(N) gauge theories

In this paper we study the topological susceptibility of two-dimensional $U(N)$ gauge theories. We provide explicit expressions for the partition function and the topological susceptibility at finite lattice spacing and finite volume. We then examine the particularly simple case of the abelian $U(1)$ theory, the continuum limit, the infinite volume limit, and we finally discuss the large $N$ limit of our results.Comment: 11 pages, 7 eps figure

Topological critical slowing down: variations on a toy model

Numerical simulations of lattice quantum field theories whose continuum counterparts possess classical solutions with non-trivial topology face a severe critical slowing down as the continuum limit is approached. Standard Monte-Carlo algorithms develop a loss of ergodicity, with the system remaining frozen in configurations with fixed topology. We analyze the problem in a simple toy model, consisting of the path integral formulation of a quantum mechanical particle constrained to move on a circumference. More specifically, we implement for this toy model various techniques which have been proposed to solve or alleviate the problem for more complex systems, like non-abelian gauge theories, and compare them both in the regime of low temperature and in that of very high temperature. Among the various techniques, we consider also a new algorithm which completely solves the freezing problem, but unfortunately is specifically tailored for this particular model and not easily exportable to more complex systems.Comment: 18 pages, 14 eps figures. Some changes and references added. To be published by Phys Rev

Phase diagram of the 4D U(1) model at finite temperature

We explore the phase diagram of the 4D compact U(1) gauge theory at finite temperature as a function of the gauge coupling and of the compactified Euclidean time dimension L_t. We show that the strong-to-weak coupling transition, which is first order at T=0 (L_t=\infty), becomes second order for high temperatures, i.e. for small values of L_t, with a tricritical temporal size \bar{L_t} located between 5 and 6. The critical behavior around the tricritical point explains and reconciles previous contradictory evidences found in the literature.Comment: minor changes, version published on Phys. Rev.

The three-dimensional, three state Potts model in a negative external field

We investigate the critical behaviour of the three-dimensional, three state Potts model in presence of a negative external field h, i.e. disfavouring one of the three states. A genuine phase transition is present for all values of |h|, corresponding to the spontaneous breaking of a residual Z_2 symmetry. The transition is first/second order respectively for small/large values of |h|, with a tricritical field h_tric separating the two regimes. We provide, using different and consistent approaches, a precise determination of h_tric; we also compare with previous studies and discuss the relevance of our investigation to analogous studies of the QCD phase diagram in presence of an imaginary chemical potential.Comment: 11 pages, 17 figures, minor correction