arXiv subjects

M. Caselle

Publications and source records attributed to M. Caselle.

At least 91 records · Page 5Linked to original sources

arXiv1996

Toward an analytic determination of the deconfinement temperature in SU(2) L.G.T.

We consider the SU(2) lattice gauge theory at finite temperature in (d+1) dimensions, with different couplings $β_t$ and $β_s$ for timelike and spacelike plaquettes. By using the character expansion of the Wilson action and performing the integrals over space-like link variables, we find an effective action for the Polyakov loops which is exact to all orders in $β_t$ and to the first non-trivial order in $β_s$. The critical coupling for the deconfinement transition is determined in the (3+1) dimensional case, by the mean field method, for different values of the lattice size $N_t$ in the compactified time direction and of the asymmetry parameter $ρ= \sqrt{β_t/β_s}$. We find good agreement with Montecarlo simulations in the range $1\leq N_t \leq 5$, and good qualitative agreement in the same range with the logarithmic scaling law of QCD. Moreover the dependence of the results from the parameter $ρ$ is in excellent agreement with previous theoretical predictions.

hep-lat↗

arXiv1996

Recent results in high temperature lattice gauge theories

We review some analytic results on the deconfinement transition in pure lattice gauge theories. In particular we discuss the relationship between the deconfinement transition in the $(d+1)$-dimensional $SU(2)$ model and the magnetization transition in the $d$-dimensional Ising model. This analysis leads to a precise estimate of the deconfinement temperature which agrees well with that obtained with a Montecarlo simulation in the case in which the lattice has only one link in the compactified time direction.

hep-lat↗

arXiv1995

Deconfinement transition and dimensional cross-over in the 3D gauge Ising model

We present a high precision Monte Carlo study of the finite temperature $Z_2$ gauge theory in 2+1 dimensions. The duality with the 3D Ising spin model allows us to use powerful cluster algorithms for the simulations. For temporal extensions up to $N_t=16$ we obtain the inverse critical temperature with a statistical accuracy comparable with the most accurate results for the bulk phase transition of the 3D Ising model. We discuss the predictions of T. W. Capehart and M.E. Fisher for the dimensional crossover from 2 to 3 dimensions. Our precise data for the critical exponents and critical amplitudes confirm the Svetitsky-Yaffe conjecture. We find deviations from Olesen's prediction for the critical temperature of about 20%.

hep-lat↗

arXiv1995

Width of Long Colour Flux Tubes in Lattice Gauge Systems

In the confining phase of any gauge system the mean squared width of the colour flux tube joining a pair of quarks should grow logarithmically as a function of their distance, according to the effective string description of its infrared properties. New data on 3D Z_2 gauge theory, combined with high precision data on the interface physics of the 3D Ising model fit nicely this behaviour over a range of more than two orders of magnitude.

hep-lat↗

arXiv1995

Calogero-Sutherland techniques in the physics of disorderd wires

We discuss the connection between the random matrix approach to disordered wires and the Calogero-Sutherland models. We show that different choices of random matrix ensembles correspond to different classes of CS models. In particular, the standard transfer matrix ensembles correspond to CS model with sinh-type interaction, constructed according to the $C_n$ root lattice pattern. By exploiting this relation, and by using some known properties of the zonal spherical functions on symmetric spaces we can obtain several properties of the Dorokhov-Mello-Pereyra-Kumar equation, which describes the evolution of an ensemble of quasi one-dimensional disordered wires of increasing length $L$. These results are in complete agreement with all known properties of disordered wires. (To appear in the Proceedings of the Conference: Recent Developments in Statistical Mechanics and Quantum Field Theory (Trieste, 1995))

cond-mat↗

arXiv1995

A new universality class describing the insulating regime of disordered wires with strong spin-orbit scattering

We discuss the distribution of transmission eigenvalues in the strongly localized regime in the presence of both a magnetic field and spin--orbit scattering. We show that, under suitable conditions, this distribution can be described by a new universality class labelled not only by the index $β$ but also by a new index $η$. This result is obtained by mapping the problem into that of a suitable Calogero-Sutherland model.

cond-mat↗

arXiv1995

Some Analytical Results in (2+1) dimensional L.G.T.

We show that, within the framework of suitably chosen approximate effective actions it is possible to evaluate analytically the string tension, the spacelike string tension and the deconfinement temperature of (2+1) dimensional lattice gauge theories. In the case of SU(2) gauge theory our results agree with those obtained through Montecarlo simulations.

hep-lat↗

arXiv1995

On the distribution of transmission eigenvalues in disordered wires

We solve the Dorokhov-Mello-Pereyra-Kumar equation which describes the evolution of an ensamble of disordered wires of increasing length in the three cases $β=1,2,4$. The solution is obtained by mapping the problem in that of a suitable Calogero-Sutherland model. In the $β=2$ case our solution is in complete agreement with that recently found by Beenakker and Rejaei.

cond-mat↗

arXiv1994

The Width of the Colour Flux Tube

We discuss and rederive in a general way the logarithmic growth of the mean squared width of the colour flux tube as a function of the interquark separation. Recent data on 3D $Z_2$ gauge theory, combined with high precision data on the interface physics of the 3D Ising model fit nicely this behaviour over a range of more than two orders of magnitude.

hep-lat↗

arXiv1994

Rough Interfaces Beyond the Gaussian Approximation

We compare predictions of the Capillary Wave Model with Monte Carlo results for the energy gap and the interface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two-loop order (one order beyond the Gaussian approximation).

hep-lat↗

arXiv1994

Deconfinement Transition in Large N Lattice Gauge Theory

We study analytically the phase diagram of the pure $SU(N)$ lattice gauge theory at finite temperature, and we attempt to estimate the critical deconfinement temperature. We apply large $N$ techniques to the Wilson and to the Heat Kernel action, and we study the resulting models both in the strong coupling and in the weak coupling limits. Using the Heat Kernel action, we establish an interesting connection between the Douglas-Kazakov phase transition of two-dimensional QCD and the deconfining transition in $d$ dimensions. The analytic results obtained for the critical temperature compare well with Montecarlo simulations of the full theory in $(2+1)$ and in $(3+1)$ dimensions.

hep-lat↗

arXiv1994

Fluid Interfaces in the 3D Ising Model as a Dilute Gas of Handles

We study the topology of fluid interfaces in the 3D Ising model in the rough phase. It turns out that such interfaces are accurately described as dilute gases of microscopic handles, and the stiffness of the interface increases with the genus. The number of configurations of genus $g$ follows a Poisson-like distribution. The probability per unit area for creating a handle is well fitted in a wide range of the inverse temperature $β$ near the roughening point by an exponentially decreasing function of $β$. The procedure of summing over all topologies results in an effective interface whose squared width scales logarithmically with the lattice size.

cond-mat↗

arXiv1994

Rough Interfaces Beyond the Gaussian Approximation

We compare predictions of the Capillary Wave Model beyond its Gaussian approximation with Monte Carlo results for the energy gap and the surface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two--loop order ( one order beyond the Gaussian approximation).

hep-lat↗

arXiv1994

The Spatial String Tension in High Temperature Lattice Gauge Theories

We develop some techniques which allow an analytic evaluation of space-like observables in high temperature lattice gauge theories. We show that such variables are described extremely well by dimensional reduction. In particular, by using results obtained in the context of ``Induced QCD'', we evaluate the contributions to space-like observables coming from the Higgs sector of the dimensionally reduced action, we find that they are of higher order in the coupling constant compared to those coming from the space-like action and hence neglegible near the continuum limit. In the case of SU(2) gauge theory our results agree with those obtained through Montecarlo simulations both in (2+1) and (3+1) dimensions and they also indicate a possible way of removing the gap between the two values of $g^2(T)$ recently appeared in the literature.

hep-lat↗

arXiv1994

On the relation between the width of the flux tube and $T_c^{-1}$ in lattice gauge theories

Within the framework of a quantum flux tube model for the interquark potential it is possible to predict that in (2+1) dimensions the space-like string tension must increase with the temperature in the deconfined phase and that the thickness of the flux tube must coincide with the inverse of the deconfinement temperature. Both these predictions are in good agreement with some recent numerical simulations of SU(2) and $Z_2$ gauge models.

hep-lat↗

arXiv1994

Finite Size Effects in Fluid Interfaces

It is shown that finite size effects in the free energy of a rough interface of the 3D Ising and three--state Potts models are well described by the capillary wave model at {\em two--loop} order. The agreement between theoretical predictions and Monte Carlo simulations strongly supports the idea of the universality of this description of order--order interfaces in 3D statistical systems above the roughening temperature.

hep-lat↗

arXiv1994

Self-avoiding random surfaces with fluctuating topology

A gas of self-avoiding surfaces with an arbitrary polynomial coupling to the gaussian curvature and an extrinsic curvature term can be realized in a three-dimensional Ising bcc lattice with only three local couplings. Similar three parameter realizations are valid also in other lattices. The relation between the crumpling transition and the roughening is discussed. It turns out that the mean area of these surfaces is proportional to its genus.

hep-lat↗

arXiv1993

On the behaviour of spatial Wilson loops in the high temperature phase of Lattice Gauge Theories

The behaviour of the space-like string tension in the high temperature phase is studied. Data obtained in the $Z_2$ gauge model in (2+1) dimensions are compared with predictions of a simple model of a fluctuating flux tube with finite thickness. It is shown that in the high temperature phase contributions coming from the fluctuations of the flux tube vanish. As a consequence we also show that in (2+1) dimensional gauge theories the thickness of the flux tube coincides with the inverse of the deconfinement temperature.

hep-lat↗