1,721,092 research outputs found
The Peierls argument for higher dimensional Ising models
No full textThe 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 dimensions. The aim of this paper is to present an elementary discussion of the Peierls argument for the general D-dimensional Ising model. © 2014 IOP Publishing Ltd
Variations in the magnetic torque acting on a wire
No full textThe relation M = Î1⁄4 à B is presented in all elementary courses on electromagnetism, but it is usually given just for the simple case of a rectangular wire. We will present a completely general but elementary proof of this relation together with two more advanced proof methods. We will then provide some extensions: non-closed wires and non-uniform magnetic field. © 2012 IOP Publishing Ltd
Topology and θ dependence in finite temperature G2 lattice gauge theory
Full text linkAbstract: In this work we study the topological properties of the G2 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 Î ̧ 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 > Tc
Finite temperature effective string corrections in (3+1)D SU(2) lattice gauge theory
No full textWe study the effective string corrections to the inter-quark potential at finite temperature by simulating the SU(2) lattice gauge theory in four dimensions. We provide the first numerical evidence that the logarithmic correction to the potential, which was recently proposed to be a signature of the effective string at finite temperature, is universal also in (3+1)D gauge theory, thus extending previous results limited to the (2+1)D case. © 2011 Elsevier B.V
On the phase diagram of the 4D U(1) model at finite temperature
No full textWe 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
Color-flavor reflection in the continuum limit of two-dimensional lattice gauge theories with scalar fields
Full text linkWe address the interplay between local and global symmetries in determining
the continuum limit of two-dimensional lattice scalar theories characterized by
gauge symmetry and non-Abelian global invariance. We argue
that, when a quartic interaction is present, the continuum limit of these model
corresponds in some cases to the gauged non-linear model field theory
associated with the real Grassmannian manifold ), which is characterized by the invariance under the color-flavor
reflection . Monte Carlo simulations and
Finite-Size Scaling analyses, performed for and several values of
, confirm the emergence of the color-flavor reflection symmetry in the
scaling limit, and support the identification of the continuum limit.Comment: 9 pages, 8 pdf figure
Comparison of the gradient flow with cooling in SU (3) pure gauge theory
No full textThe gradient (Wilson) flow has been introduced recently in order to provide a solid theoretical framework for the smoothing of ultraviolet noise in lattice gauge configurations. It is interesting to ask how it compares with other, more heuristic and numerically cheaper smoothing techniques, such as standard cooling. In this study we perform such a comparison, focusing on observables related to topology. We show that, already for moderately small lattice spacings, standard cooling and the gradient flow lead to equivalent results, both for average quantities and configuration by configuration
Topological critical slowing down: Variations on a toy model
Full text linkNumerical simulations of lattice quantum field theories whose continuum counterparts possess classical solutions with nontrivial 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 propose an alternative algorithm which completely solves the freezing problem, but unfortunately is specifically tailored for this particular model and not easily exportable to more complex systems
The Maximal Abelian Gauge in SU(N) Gauge Theories and Thermal Monopoles for N = 3
No full textWe discuss and propose a proper extension of the Abelian projection based on
the Maximal Abelian Gauge to SU(N) gauge theories. Based, on that, we
investigate the properties of thermal Abelian monopoles in the deconfined phase
of the SU(3) pure gauge theory. Such properties are very similar to those
already found for SU(2), confirming the relevance of the magnetic component
close to Tc and the possible condensation of thermal monopoles as the
deconfinement temperature is crossed from above. Moreover, we study the
correlation functions among monopoles related to different U(1) subgroups,
which show interesting features and reveal the presence of non-trivial
interactions
The topological properties of QCD at high temperature: problems and perspectives
Full text linkLattice 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
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