arXiv subjects

Vinod Mamale

Publications and source records attributed to Vinod Mamale.

7 recordsLinked to original sources

arXiv2026

Configurational Temperature in Matrix Models and Random Matrix Ensembles

We investigate the configurational temperature estimator in interacting matrix models and Gaussian random-matrix ensembles. The estimator follows from an exact Schwinger--Dyson identity and may be expressed in terms of the gradient and Hessian of the action. We study the Gross--Witten--Wadia model, a quartic double-well matrix model, and the Gaussian Orthogonal, Unitary, and Symplectic Ensembles. In all cases, the estimator satisfies the exact Schwinger--Dyson identity, $\beta_{\rm config} = 1$, within statistical uncertainties. Separating the estimator into isotropic and anisotropic parts, we find that the leading finite-$N$ corrections satisfy the approximate relation $\beta_{\rm iso} - 1 \simeq - \beta_{\rm aniso}$. We also show that the configurational temperature estimator provides a sensitive diagnostic of Monte Carlo simulations.

hep-th↗

arXiv2025

Topological Strings in SU(3) Gauge Theory at Finite Temperature

We investigate string configurations in the deconfined phase of SU(3) gauge theory, which arise from the spontaneous breaking of the $Z_3$ center symmetry. These configurations form at the junctions of domain walls of the theory. The complex phase of the Polyakov loop changes by multiples of $2\pi$ on large spatial loops around the string, rendering them topologically stable. Using the Monte Carlo simulations of the partition function, we compute the free energy associated with these configurations. The simulations are performed on lattices with spatial dimensions $N_{x,y}=60, N_z=4$, and temporal extent $N_\tau=2$. Our results show that the free energy of the $Z_3-$strings is dominated by the domain walls. Further near the transition point, thermal fluctuations cause the decay of domain walls as well as the $Z_3$ strings into confined-deconfined interfaces.

hep-lat↗

arXiv2024

Parametric resonance in abelian and non-abelian gauge fields via space-time oscillations

We study the evolution of abelian $U(1)$ electromagnetic as well as non-abelian $SU(2)$ gauge fields, in the presence of space-time oscillations. Analysis of the time evolution of abelian gauge fields shows the presence of parametric resonance in spatial modes. A similar analysis in the case of non-abelian gauge fields, in the linear approximation, shows the presence of the same resonant spatial modes. The resonant modes induce large fluctuations in physical observables including those that break the $CP-$symmetry. We also carry out time evolution of small random fluctuations of the gauge fields, using numerical simulations in $2+1$ and $3+1$ dimensions. These simulations help to study non-linear effects in the case of non-abelian gauge theories. Our results show that there is an increase in energy density with the coupling, at late times. These results suggest that gravitational waves may excite non-abelian gauge fields more efficiently than electromagnetic fields. Also, gravitational waves in the early Universe and from the merger of neutron stars, black holes etc. may enhance $CP-$violation and generate an imbalance in chiral charge distributions, magnetic fields etc.

hep-ph↗

arXiv2023

Confinement-deconfinement transition in $SU(3)$-Higgs theory

We study lattice cutoff effects on the confinement-deconfinement transition and the $Z_3$ symmetry in $SU(3)$-Higgs theory in $3+1$ dimensions. The Higgs in this study is a complex triplet with vanishing bare mass and quartic coupling. The lattice cutoff is regulated by varying the number of temporal lattice sites, $N_τ$. Our results show that the nature of the confinement-deconfinement transition depends on $N_τ$. For $N_τ=2$ the transition is found to be the end point of a first-order transition and is first order for $N_τ\ge 3$. The distributions of the Polyakov loop and other observables, sensitive to the $Z_3$ symmetry, show that the strength of $Z_3$ explicit breaking decreases with $N_τ$. Up to $T\simeq 2T_c$, the free energy difference between $Z_3$ states decreases with $N_τ$, suggesting the realization of $Z_3$ symmetry in the continuum limit.

hep-lat↗

arXiv2022

Effect of fluctuations on the Geodesic rule for topological defect formation

At finite temperature, the field along a linear stretch of correlation length size is supposed to trace the shortest path in the field space given the two end point values, known as the Geodesic rule. In this study, we compute the probability that, the field variations over distances of correlation length follow this rule in theories with $O(2)$ global symmetry. We consider a simple ferromagnetic $O(2)$ spin-model and a complex $ϕ^4$ theory. The computations are carried out on an ensemble of equilibrium configurations, generated using Monte Carlo simulations. The numerical results suggest significant deviation to the Geodesic rule, relevant for formation of topological defects during quench in 2nd order phase transition. Also for the case of $O(2)-$spins in two dimensions, distribution and density of vortices, have been studied. It is found that, for quench temperatures close to the transition point, the Kibble-Zurek Mechanism underestimates equilibrium density of defects. The exponents corresponding to width of the distributions, are found to be smaller than Kibble Mechanism estimates and match only when there is no deviation from the geodesic rule.

hep-ph↗

arXiv2021

$Z_N$ symmetry in $SU(N)$ gauge theories

We study $Z_N$ symmetry in $SU(N)$ gauge theories in the presence of matter fields in the fundamental representation, by restricting the lattice partition function integration to matter fields which are uniform in spatial directions and gauge fields with vanishing spatial components. In this approximation the gauge matter field interaction effectively reduces to a 1-dimensional gauged chain. This makes analytical calculations of the matter field contribution to the Polyakov loop free energy possible. We show that in the limit of large number of temporal sites the explicit breaking of $Z_N$ symmetry in this free energy vanishes, driven by dominance of the density of states. We argue that the spatial links as well as the spatial modes of the matter fields determine the boundaries separating regions where $Z_N$ symmetry is realised from rest of the phase diagram.

hep-lat↗

arXiv2021

Confinement-Deconfinement transition and $Z_2$ symmetry in $Z_2+$Higgs theory

We study the Polyakov loop and the $Z_2$ symmetry in the lattice $Z_2+$Higgs theory in 4D Euclidean space using Monte Carlo simulations. The results show that this symmetry is realised in the Higgs symmetric phase for large number of temporal lattice sites. To understand the dependence on the number of temporal sites, we consider a one dimensional model by keeping terms of the original action corresponding to a single spatial site. In this approximation the partition function can be calculated exactly as a function of the Polyakov loop. The resulting free energy is found to have the $Z_2$ symmetry in the limit of large temporal sites. We argue that this is due to $Z_2$ invariance as well as dominance of the distribution or density of states corresponding to the action.

hep-lat↗