arXiv subjects

Bharadwaj Vedula

Publications and source records attributed to Bharadwaj Vedula.

5 recordsLinked to original sources

arXiv2026

The Phase Transitions in a $p$ spin Glass Model: A Numerical Study

We investigate the balanced $M=4$, $p=4$ spin-glass model for a one-dimensional long-range proxy for the finite dimensional short-range $p$-spin glass model to examine the nature of the glass transition beyond mean-field theory. We perform large-scale Monte Carlo equilibrated simulations for both fully connected and power-law diluted versions of the model. The critical temperatures extracted from the finite-size scaling (FSS) analysis of spin-glass susceptibility are in good agreement with theoretical predictions for $σ= 0, 0.25$, and 0.55. For these values of the long-range exponent $σ$ (which is the power of the decrease of the interactions between the spins with their separation), one might have expected that mean-field theory would provide a good description of the system. However, the spin-overlap distribution and the value of the $λ$-parameter do not provide numerical evidence for a one-step replica symmetry breaking (1RSB) phase transition. Instead, our results indicate a direct transition from the paramagnetic state to a full replica symmetry broken phase, with a renormalized value of $λ\equiv ω_2/ω_1 < 1$ suggesting a continuous FRSB transition, despite this ratio being equal to 2 at mean-field level. A value of $λ> 1$ is required for the discontinuous 1RSB transition. We argue that strong finite-size effects and closely spaced transition temperatures remove the expected 1RSB transition for the system sizes which we can study. For values of the exponent $σ= 0.85$, which roughly corresponds to a three dimensional system, we find that the renormalized value of $λ$ is again less than 1, with no signs of either the 1RSB transition or the continuous FRSB transition, suggesting that the Kauzmann temperature $T_K$ in three dimensions might be zero and the complete absence of phase transitions in structural glasses.

cond-mat.dis-nn↗

arXiv2026

Entanglement entropy as a probe of topological phase transitions

Entanglement entropy (EE) provides a powerful probe of quantum phases, yet its role in identifying topological phase transitions in disordered systems remains underexplored. We introduce an exact EE-based framework that captures topological phase transitions even in the presence of disorder. Specifically, for a class of Su-Schrieffer-Heeger (SSH) model variants, we show that the difference in EE between half-filled and near-half-filled ground states, $ΔS^{\mathcal{A}}$, vanishes in the topological phase but remains finite in the trivial phase, a direct consequence of edge-state localization. This behavior persists even in the presence of quasiperiodic or binary disorder. By analyzing domain-wall configurations in the SSH chain, we further show how subsystem tuning allows one to distinguish genuine topological zero-energy eigenstates from trivial localized states. Exact phase boundaries, derived from Lyapunov exponents via transfer matrices, agree closely with numerical results from $ΔS^{\mathcal{A}}$ and the topological invariant $\mathcal{Q}$, with instances where $ΔS^{\mathcal{A}}$ outperforms $\mathcal{Q}$. Our results highlight EE as a robust diagnostic tool and a potential bridge between quantum information and condensed matter approaches to topological matter.

cond-mat.str-el↗

arXiv2024

Nature of spin glass order in physical dimensions

We have studied the diluted Heisenberg spin glass model in a 3-component random field for the commonly-used one-dimensional long-range model where the probability that two spins separated by a distance $r$ interact with one another falls as $1/r^{2 σ}$, for two values of $σ$, $0.75$ and $0.85$. No de Almeida-Thouless line is expected at these $σ$ values. The spin glass correlation length $ξ_{\text{SG}}$ varies with the random field as expected from the Imry-Ma argument and the droplet scaling picture of spin glasses. However, when $ξ_{\text{SG}}$ becomes comparable to the system size $L$, there are departures which we attribute to the features deriving from the TNT picture of spin glasses. For the case $σ=0.85$ these features go away for system sizes with $L >L^*$, where $L^*$ is large ($\approx 4000-8000$ lattice spacings). In the case of $σ= 0.75$ we have been unable to study large enough systems to determine its value of $L^*$. We sketch a renormalization group scenario to explain how these features could arise. On this scenario finite size effects on the droplet scaling picture in low-dimensional spin glasses produce TNT features and some aspects of Parisi's replica symmetry breaking theory of the Sherrington-Kirkpatrick model.

cond-mat.dis-nn↗

arXiv2024

Evidence that the AT transition disappears below six dimensions

One of the key predictions of Parisi's broken replica symmetry theory of spin glasses is the existence of a phase transition in an applied field to a state with broken replica symmetry. This transition takes place at the de Almeida-Thouless (AT) line in the $h-T$ plane. We have studied this line in the power-law diluted Heisenberg spin glass in which the probability that two spins separated by a distance $r$ interact with each other falls as $1/r^{2σ}$. In the presence of a random vector-field of variance $h_r^2$ the phase transition is in the universality class of the Ising spin glass in a field. Tuning $σ$ is equivalent to changing the dimension $d$ of the short-range system, with the relation being $d =2/(2σ-1)$ for $σ< 2/3$. We have found by numerical simulations that $h_{\text{AT}}^2 \sim (2/3 -σ)$ implying that the AT line does not exist below $6$ dimensions and that the Parisi scheme is not appropriate for spin glasses in three dimensions.

cond-mat.dis-nn↗

arXiv2023

Study of the de Almeida-Thouless (AT) line in the one-dimensional diluted power-law XY spin glass

We study the AT line in the one-dimensional power-law diluted XY spin glass model, in which the probability that two spins separated by a distance $r$ interact with each other, decays as $1/r^{2σ}$. We develop a heat bath algorithm to equilibrate XY spins; using this in conjunction with the standard parallel tempering and overrelaxation sweeps, we carry out large scale Monte Carlo simulations. For $σ=0.6$ which is in the mean-field regime, we find clear evidence for an AT line. For $σ= 0.75$, there is evidence from finite size scaling studies for an AT transition but for $σ= 0.85$, the evidence for a transition is non-existent. We have also studied these systems at fixed temperature varying the field and discovered that at both $σ= 0.75$ and at $σ=0.85$ there is evidence of an AT transition! Confusingly, the correlation length and spin glass susceptibility as a function of the field are both entirely consistent with the predictions of the droplet picture and hence the non-existence of an AT line. The evidence from our simulations points to the complete absence of the AT line in dimensions outside the mean-field region and to the correctness of the droplet picture. Previous simulations which suggested there was an AT line can be attributed to the consequences of studying systems which are just too small. The collapse of our data to the droplet scaling form is poor for $σ= 0.75$ and to some extent also for $σ= 0.85$, when the correlation length becomes of the order of the length of the system, due to the existence of excitations which only cost a free energy of $O(1)$, just as envisaged in the TNT picture of the ordered state of spin glasses. However, for the case of $σ= 0.85$ we can provide evidence that for larger system sizes, droplet scaling will prevail even when the correlation length is comparable to the system size.

cond-mat.dis-nn↗