Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0506578

Critical Dynamics of Dimers: Implications for the Glass Transition

Dibyendu Das·Greg Farrell·Jane' Kondev·Bulbul Chakraborty
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy vanishing phase transition, and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments and numerical diagonalizations of the master equation, we find non-exponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point, and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Dibyendu Das, Greg Farrell, Jane' Kondev, Bulbul Chakraborty. 2005-06-22. Critical Dynamics of Dimers: Implications for the Glass Transition. https://arxiv.org/abs/cond-mat/0506578

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Competition for Survival and the Law of Maximum Entropy Production

The law of maximum entropy production (LMEP) is a selection principle stating that a non-equilibrium system will select the path or assembly of paths out of available paths that minimizes the potential or maximizes the entropy at the fastest rate given the constraints. Precise quantitative experimental tests are desirable for LMEP verification. Here we report electrical-circuit experiments on suspensions of silver particles which self-organize under electric field, form conducting paths and thus generate entropy by Joule heating. Our experiments on parallel-connected pairs of samples demonstrate a competitive relationship, thereby supporting the selection of the most efficient path. We find: (1) With sufficient voltage, a conducting bundle of silver particles forms, which acts as a self-organized dissipative structure (SODS). (2) With two samples in parallel, usually only one can develop SODS, due to the competition effect. As one sample approaches the maximum EPR, the others EPR is near zero. This confirms the path selection principle: only the highest EPR path survives. (3) At the end of the evolution, the sum of the sample EPR and the power supply circuit EPR approaches the calculated maximum. The deviation from the maximum is slightly lower when there are two competing samples. We identify the selection mechanism enabling natural selection and LMEP: A SODS gains a form of physical "fitness" when it establishes a pathway that efficiently suppresses the driving thermodynamic potential. As it develops and approaches the maximum EPR, the SODS modifies its nonequilibrium environment by consuming available free energy and eliminating the gradients that could support alternative pathways. We also examine the global implications of LMEP and propose that it serves as a driving mechanism propelling the hypothetical ascent of civilizations along the Kardashev scale.

cond-mat.stat-mech↗
arXiv2026

Measurement-induced spatially nonuniform fluctuations of the local particle number and their crossover in a quasiperiodic free-fermion chain

We study continuously monitored dynamics of a quasiperiodic free-fermion chain defined on a Fibonacci lattice. We focus on fluctuations of the local particle number, which do not exhibit quasiperiodic spatial modulation in the unitary limit. Remarkably, we demonstrate that they exhibit a nonuniform spatial pattern originating from the quasiperiodic long-range order under continuous measurement. Furthermore, employing both physicaland perpendicular-space analyses, we elucidate that a measurement-induced crossover emerges in fluctuations due to the interplay between the incommensurate modulation and the continuous measurement. While weak measurement yields a distribution reflecting the long-range spatial structure of the quasiperiodic system, an increase in measurement strength alters the distribution into one dominated by the local environment of each site. A structure-factor analysis further reveals that the weak-measurement regime is characterized by two dominant Bragg peaks corresponding to the golden-mean modulation, whereas the strong-measurement regime exhibits the characteristic Bragg-peak hierarchy of the Fibonacci pattern. We also elucidate that the measurement-induced crossover emerges in other physical quantities such as connected correlation functions. These findings offer insights into nonequilibrium quasiperiodic phenomena emerging in continuously monitored dynamics.

cond-mat.stat-mech↗
arXiv2026

Entanglement Asymmetry in Random Quantum Automata

We investigate the subsystem entanglement asymmetry in random quantum automaton ensembles, which are generated by permuting the basis states in the Hilbert space and applying global phase shifts. We compute the ensemble average of the $U(1)$ subsystem asymmetry in different connectivity geometries, showing that the late-time limit of the ensemble associated to a 2-local circuit geometry coincides with the all-to-all ensemble average. By focusing on different subsystem sizes, we demonstrate that, similarly to Haar-random circuits, the system locally symmetrizes. However, in sharp contrast to the Haar-random setting, the scale at which symmetrization happens depends on the initial state, a phenomenon we associate with the interplay of conservation of the participation entropy and the uniform exploration of charge sectors. Additionally, we connect the growth of the subsystem asymmetry to the subsystem coherence and show that their growth is characterized by the same symmetrization scale.

cond-mat.stat-mech↗