arXiv subjects

Stefano Lottini

Publications and source records attributed to Stefano Lottini.

33 records · Page 2Linked to original sources

arXiv2011

Strong-coupling effective action(s) for SU(3) Yang-Mills

We apply strong-coupling expansion techniques to finite-temperature lattice pure gauge theory, obtaining dimensionally reduced $Z_N$-symmetric effective theories. The analytic mappings between the effective couplings and the original one, viz. $β$, allow to estimate the transition point $β_c$ of the 4D theory for a large range of the imaginary-time extent $N_τ$ of the lattice. We study the models for SU(3) via Monte Carlo simulation, finding satisfactory agreement with the critical point of the original theories especially at low $N_τ$. We have fixed an error in the group measure used in arXiv:1010.0951 and provide here the correct numerical results.

hep-lat↗

arXiv2011

A percolation transition in Yang-Mills matter at finite number of colours

We examine baryonic matter at quark chemical potential of the order of the confinement scale, $μ_q\sim \lqcd$. In this regime, quarks are supposed to be confined but baryons are close to the ``tightly packed limit'' where they nearly overlap in configuration space. We show that this system will exhibit a percolation phase transition {\em when varied in the number of colours} $N_c$: at high $N_c$, large distance correlations at quark level are possible even if the quarks are essentially confined. At low $N_c$, this does not happen. We discuss the relevance of this for dense nuclear matter, and argue that our results suggest a new ``phase transition'', varying $N_c$ at constant $μ_q$.

nucl-th↗

arXiv2010

Effective Polyakov-loop theory for pure Yang-Mills from strong coupling expansion

Lattice Yang-Mills theories at finite temperature can be mapped onto effective 3d spin systems, thus facilitating their numerical investigation. Using strong-coupling expansions we derive effective actions for Polyakov loops in the $SU(2)$ and $SU(3)$ cases and investigate the effect of higher order corrections. Once a formulation is obtained which allows for Monte Carlo analysis, the nature of the phase transition in both classes of models is investigated numerically, and the results are then used to predict -- with an accuracy within a few percent -- the deconfinement point in the original 4d Yang-Mills pure gauge theories, for a series of values of $N_τ$ at once.

hep-lat↗

arXiv2009

The confining string beyond the free-string approximation in the gauge dual of percolation

We simulate five different systems belonging to the universality class of the gauge dual of three-dimensional random percolation to study the underlying effective string theory at finite temperature. All the data for the finite temperature string tension, when expressed by means of adimensional variables, are nicely described by a unique scaling function. We calculate the first few terms of the string tension up to order $T^6$ and compare to different theoretical predictions. We obtain unambiguous evidence that the coefficients of $T^2$ and $T^4$ terms coincide with those of the Nambu-Goto string, as expected, while the $T^6$ term strongly differs and is characteristic of the universality class of this specific gauge theory.

hep-lat↗

arXiv2008

Confining string beyond the free approximation: the case of random percolation

The random percolation model can be viewed as the dual of a well defined confining gauge theory; since this theory, having no Monte Carlo dynamics at all, is simple to simulate, it is possible to study the properties of the flux tube with very high precision; we show it can be described by the effective string picture. Our results are lattice regularisation independent, therefore they are well defined also in the continuum limit, and, for the first time in a gauge theory, it has been possible to determine the next-to-leading quantum corrections throughout the computation of the T^6 coefficient of the Taylor expansion of sigma(T). Furthermore, this coefficient results to be related to the universal ratio T_c/\sqrt{sigma_0}.

hep-lat↗

arXiv2008

The monopole mass in the random percolation gauge theory

We study the behaviour of the monopole at finite temperature in the (2+1)-dimensional lattice gauge theory dual to the percolation model; by exploiting the correspondences to statistical systems, we possess powerful tools to evaluate the monopole mass both above and below the critical temperature with high-precision Monte Carlo simulations.

hep-lat↗

arXiv2008

The saturation threshold of public opinion: are aggressive media campaigns always effective?

An important aspect that must be considered when studying opinion formation phenomena is the different social attitude of the agents taking part in the process. Different kinds of interconnections and of interacting behaviours should be associated to the agents depending on their opinion: radicals tend to self-segregate but, on the other hand, have a stronger capacity to convince neutral agents. Other important questions arise when the official media strongly promotes one position. The different perception that each agent has of the official information can lead, in case of monopolistic and aggressive media, to a reaction effect in the population that starts to create massive antagonist clusters.

physics.soc-ph↗

arXiv2007

K-string tensions at finite temperature and integrable models

It has recently been pointed out that simple scaling properties of Polyakov correlation functions of gauge systems in the confining phase suggest that the ratios of k-string tensions in the low temperature region is constant up to terms of order T^3. Here we argue that, at least in a three-dimensional Z_4 gauge model, the above ratios are constant in the whole confining phase. This result is obtained by combining numerical experiments with known exact results on the mass spectrum of an integrable two-dimensional spin model describing the infrared behaviour of the gauge system near the deconfining transition.

hep-lat↗

arXiv2007

On the conformal anomaly of k-strings

We discuss the long distance behaviour of the flux tube associated to baryon vertices and argue that, if the gauge system admits stable k-strings, the conformal field theory describing this string in the IR has conformal anomaly c=(d-2)σ_k/σ, where σ_k is the k-string tension and σthat of the fundamental representation. We check this result in a 3D Z_4 gauge model at finite temperature, where a string effect directly related to "c" can be clearly identified.

hep-lat↗

arXiv2007

Universal properties of the confining string in the random percolation model

Random percolation can be fully interpreted as a confining pure gauge theory. With numerical high-precision measurements of Polyakov-Polyakov correlators at finite temperature, we could well observe the presence of shape effects due to rough fluctuations of the confining string, in complete agreement with the universality predictions up to the next-to-leading order.

hep-lat↗

arXiv2007

The conformal anomaly of k-strings

Simple scaling properties of correlation functions of a confining gauge theory in d-dimensions lead to the conclusion that k-string dynamics is described, in the infrared limit, by a two-dimensional conformal field theory with conformal anomaly c=(d-2)T_k/T_1, where T_k is the k-string tension. This result applies to any gauge theory with stable k-strings. We check it in a 3D Z_4 gauge model at finite temperature, where a string effect directly related to c can be clearly identified.

hep-th↗

arXiv2006

Quantum broadening of k-strings in gauge theories

We study the thickness of the confining flux tube generated by a pair of sources in higher representations of the gauge group. Using a simple geometric picture we argue that the area of the cross-section of the flux tube, as measured by a Wilson loop probe, grows logarithmically with source separation, as a consequence of the quantum fluctuations of the underlying k-string. The slope of the logarithm turns out to be universal, i.e. it is the same for all the representations and all the gauge theories. We check these predictions in a 3D Z_4 lattice gauge model by comparing the broadening of the 1-string and the 2-string.

hep-th↗

arXiv2006

Broadening of the confining flux tube joining higher-representation sources

In the context of confining gauge theories we study the flux tube generated by a pair of static sources belonging to higher rank representations of the gauge group. Using a simple geometric approach based on minimal surfaces describing the world-sheet of the underlying k-string, we infer logarithmic broadening of the flux tube as a function of source separation. It turns out that the coefficient of the logarithm does not depend on the specific representation of the source nor on its N-ality and is universal. Numerical results on a Z_4 gauge theory in three dimensions with static sources carrying two units of elementary flux compare very favourably with these predictions.

hep-lat↗

arXiv2006

Quantum fluctuations of k-strings: A case study

K strings in Yang-Mills theory can be considered as bound states of k elementary confining strings carrying one unit of colour flux. Current estimates of k-string tension sigma_k are very sensitive to the leading corrections due to quantum fluctuations of the string. In this study we address this problem by comparing Polyakov-Polyakov correlators in the fundamental representation (k=1) with the corresponding ones with k=2 in the confining phase of a Z_4 gauge theory in three dimensions. Highly efficient simulation techniques are available in this case. Although the k=1 Polyakov-Polyakov correlator matches nicely with the expected bosonic string effects up to the Next-to-Leading-Order, the k=2 Polyakov-Polyakov correlators show large deviations. This is an important source of potential systematic errors in the current estimates of sigma_k.

hep-lat↗

arXiv2005

The glue-ball spectrum of pure percolation

We present a high-precision numerical study of 3D random percolation viewed as a confining gauge theory. Using large correlation matrices among multiform Wilson loops we determine the low-lying masses in various spin channels.

hep-lat↗