arXiv subjects

J. Yeo

Publications and source records attributed to J. Yeo.

10 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 $\sigma = 0, 0.25$, and 0.55. For these values of the long-range exponent $\sigma$ (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 $\lambda$-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 $\lambda\equiv \omega_2/\omega_1 < 1$ suggesting a continuous FRSB transition, despite this ratio being equal to 2 at mean-field level. A value of $\lambda > 1$ 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 $\sigma = 0.85$, which roughly corresponds to a three dimensional system, we find that the renormalized value of $\lambda$ 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↗

arXiv2023

Replica Symmetry Broken States of some Glass Models

We have studied in detail the $M$-$p$ balanced spin glass model, especially the case $p=4$. These types of model have relevance to structural glasses. The models possess two kinds of broken replica states; those with one-step replica symmetry breaking (1RSB) and those with full replica symmetry breaking (FRSB). To determine which arises requires studying the Landau expansion to quintic order. There are 9 quintic order coefficients, and 5 quartic order coefficients, whose values we determine for this model. We show that it is only for $2 \leq M < 2.4714 \cdots$ that the transition at mean-field level is to a state with FRSB, while for larger $M$ values there is either a continuous transition to a state with 1RSB (when $ M \leq 3$) or a discontinuous transition for $M > 3$. The Gardner transition from a 1RSB state at low temperatures to a state with FRSB also requires the Landau expansion to be taken to quintic order. Our result for the form of FRSB in the Gardner phase is similar to that found when $2 \leq M < 2.4714\cdots$, but differs from that given in the early paper of Gross et al. [Phys. Rev. Lett. 55, 304 (1985)]. Finally we discuss the effects of fluctuations on our mean-field solutions using the scheme of Höller and Read [Phys. Rev. E 101, 042114 (2020)}] and argue that such fluctuations will remove both the continuous 1RSB transition and discontinuous 1RSB transitions when $8 >d \geq 6$ leaving just the FRSB continuous transition. We suggest values for $M$ and $p$ which might be used in simulations to confirm whether fluctuation corrections do indeed remove the 1RSB transitions.

cond-mat.dis-nn↗

arXiv2020

Possible instability of one-step replica symmetry breaking in p-spin Ising models outside mean-field theory

The fully-connected Ising $p$-spin model has for $p >2$ a discontinuous phase transition from the paramagnetic phase to a stable state with one-step replica symmetry breaking (1RSB). However, simulations in three dimension do not look like these mean-field results and have features more like those which would arise with full replica symmetry breaking (FRSB). To help understand how this might come about we have studied in the fully connected $p$-spin model the state of two-step replica symmetry breaking (2RSB). It has a free energy degenerate with that of 1RSB, but the weight of the additional peak in $P(q)$ vanishes. We expect that the state with full replica symmetry breaking (FRSB) is also degenerate with that of 1RSB. We suggest that finite size effects will give a non-vanishing weight to the FRSB features, as also will fluctuations about the mean-field solution. Our conclusion is that outside the fully connected model in the thermodynamic limit, FRSB is to be expected rather than 1RSB.

cond-mat.dis-nn↗

arXiv2006

An Improved Nonperturbative Method for Studying Two-dimensional Vortex Liquids

We show how a systematic improvement can be made on the nonperturbative parquet approximation method which was previously used to study the effect of thermal fluctuations in vortex liquids in high-temperature superconductors. This is achieved by including an infinite subset of Feynman diagrams contributing to the renormalized four-point vertex function of the Ginzburg-Landau model, which was omitted in the original approximation. We find that the growing crystalline order in the vortex liquid is more pronounced in the improved approximation. In particular, the second and third peaks in the liquid structure factor, which appeared as one peak in the original approximation, are now resolved.

cond-mat.supr-con↗

arXiv2006

The Thermodynamic Glass Transition in Finite Dimensions

Using an effective potential method, a replica formulism is set up for describing supercooled liquids near their glass transition. The resulting potential is equivalent to that for an Ising spin glass in a magnetic field. Results taken from the droplet picture of spin glasses are then used to provide an explanation of the main features of fragile glasses.

cond-mat.dis-nn↗

arXiv2005

Reconstruction of condensed magnetoexciton droplet in a trap in strong magnetic fields

We investigate theoretically the Bose-Einstein condensation of trapped magnetoexcitons in a two-layered system with one layer containing electrons and the other layer containing holes. We have studied the spatial variations of the condensate density in the droplet of electrons and holes. We find that the shape of the electron and hole densities may change due to the competition between repulsive electron-electron/hole-hole interaction and confinement potential of the trap. Our mean field calculations show that when the confinement strength is strong enough the condensate density is peaked at the edge of the droplet, and as the confinement strength weakens the condensate density displays one inner peak and another peak at the edge. For much weaker confinement potential the condensate density may display one broad peak.

cond-mat.mes-hall↗

arXiv2005

Nature of perturbation theory in spin glasses

The high-order behavior of the perturbation expansion in the cubic replica field theory of spin glasses in the paramagnetic phase has been investigated. The study starts with the zero-dimensional version of the replica field theory and this is shown to be equivalent to the problem of finding finite size corrections in a modified spherical spin glass near the critical temperature. We find that the high-order behavior of the perturbation series is described, to leading order, by coefficients of alternating signs (suggesting that the cubic field theory is well-defined) but that there are also subdominant terms with a complicated dependence of their sign on the order. Our results are then extended to the d-dimensional field theory and in particular used to determine the high-order behavior of the terms in the expansion of the critical exponents in a power series in epsilon=6-d. We have also corrected errors in the existing epsilon expansions at third order.

cond-mat.dis-nn↗

arXiv2004

The Complexity of Vector Spin Glasses

We study the annealed complexity of the m-vector spin glasses in the Sherrington-Kirkpatrick limit. The eigenvalue spectrum of the Hessian matrix of the Thouless-Anderson-Palmer (TAP) free energy is found to consist of a continuous band of positive eigenvalues in addition to an isolated eigenvalue and (m-1) null eigenvalues due to rotational invariance. Rather surprisingly, the band does not extend to zero at any finite temperature. The isolated eigenvalue becomes zero in the thermodynamic limit, as in the Ising case (m=1), indicating that the same supersymmetry breaking recently found in Ising spin glasses occurs in vector spin glasses.

cond-mat.dis-nn↗

arXiv2003

Bose-Einstein condensate of two-dimensional excitons in a ring: Necklace-like modulation of order parameter

We have studied theoretically the Bose-Einstein condensation (BEC) of two-dimensional excitons in a ring with small random width variation. We derive a nonlinear Gross-Pitaevkii equation (GPE) for such a condensate. Our numerical solution of the ground state of the GPE displays a necklace-like structure in the presence of small random variation of ring width. This is a consequence of the interplay between random potential and the nonlinear repulsive term of the GPE. Our result suggests that the formation of ring and necklace-like structures observed recently in the photoluminescence of quantum wells may be stable even in the BEC phase.

cond-mat.str-el↗

arXiv2002

Reentrant Melting of Soliton Lattice Phase in Bilayer Quantum Hall System

At large parallel magnetic field $B_\parallel$, the ground state of bilayer quantum Hall system forms uniform soliton lattice phase. The soliton lattice will melt due to the proliferation of unbound dislocations at certain finite temperature leading to the Kosterlitz-Thouless (KT) melting. We calculate the KT phase boundary by numerically solving the newly developed set of Bethe ansatz equations, which fully take into account the thermal fluctuations of soliton walls. We predict that within certain ranges of $B_\parallel$, the soliton lattice will melt at $T_{\rm KT}$. Interestingly enough, as temperature decreases, it melts at certain temperature lower than $T_{\rm KT}$ exhibiting the reentrant behaviour of the soliton liquid phase.

cond-mat.mes-hall↗