arXiv subjects

Diana Thongjaomayum

Publications and source records attributed to Diana Thongjaomayum.

12 recordsLinked to original sources

arXiv2026

Analysis of spin avalanches due to interplay of disorder and temperature

The nonequilibrium zero-temperature Random Field Ising Model (RFIM) has been extensively studied to understand critical response and avalanches in disordered driven systems. The emergence of power-law behaviour is observed over a wide region around the critical point. These studies however, are confined to zero-temperature dynamics. We study the role of temperature, which is inevitable in real experiments, in the context of RFIM on triangular lattices. We explore the interplay of different parameters: temperature, random field strength, and relaxation time which affect the prevalence of power-law behaviour on the lattice. The results indicate that power-law survives only in the regime of low temperature or small and intermediate disorder. Variations in temperature and disorder have similar affects on the avalanche-size distribution, indicating their strong correspondence. We also discuss the process of blurring out of the power law on increasing temperature or disorder.

cond-mat.dis-nn↗

arXiv2026

Understanding jump discontinuity in disordered system

The response of a complex system to a slow varying external force often displays a jump discontinuity in the order parameter near the critical point. However, this discontinuity is not usually a single jump but rather breaks into smaller jumps which makes it difficult to locate the critical point on approaching its vicinity based only on simulations, in the absence of exact results. Our work is a small effort in understanding these breaks in jump through the hysteretic response of a classical Ising spin system to an external field, $h$, in the context of a nonequilibrium zero-temperature random field Ising model on dilute systems. We consider a Bethe lattice with coordination number, $z = 4$, and dilute a fraction $(1-c)$ of the sites. Therefore the lattice now consists of sites with varying $z = 4, 3, 2, 1$ and possibly few isolated sites $(z=0)$, depending on the concentration $c$. We obtain the exact solution of the magnetization curve, $m(h)$ vs $h$, for the entire lattice as well as for each sublattice of different $z$ coordinated sites, $m_4(h), m_3(h), m_2(h), m_1(h), m_0(h)$. The discontinuity in total magnetization is the result of the superposition of the jumps of different $z$ coordinated sites and observed at the same value of external field, $h_{crit}$. The dominant contribution to the jump comes from those sites with higher concentration and larger $z$. However, the triggering sites responsible for large jumps are mostly $z\ge3$. We test this on cubic lattices as well, where exact results are not available. We hope our analysis will help in understanding fluctuations around a jump in numerical simulations as well as experiments.

cond-mat.dis-nn↗

arXiv2026

Exploring the role of connectivity in disordered system

We study a minimal model of disordered systems, the random field Ising model (RFIM) on a generalized Petersen Graph, GP(N,k). This graph has a connected inner and outer loop, where both the loops consist of N nodes constituting a total of 2N nodes. The parameter k satisfies the condition 1<=k<=N/2, such that any site i in the inner loop has i-k and i+k as its two nearest neighbours, apart from its connection to a node on the outer loop. Thus, each node in GP(N,k) has coordination number z=3, and by varying k different connections between the nodes in the inner loop can be obtained. The objective is to study whether different connectivity between nodes in these graphs affects the system's response to an external field when the coordination number is fixed. This is of interest because critical behaviour is absent for z<=3 on a random graph which has been solved exactly as well as on the honeycomb lattice in the context of RFIM. Using single-spin-flip Glauber dynamics at zero temperature, we compare the system's response with the known case of a z=3 random graph and the generalized Petersen graph for various connectivity k, albeit for the same z. Our study finds the absence of critical behaviour on GP(N,k) highlighting the importance of coordination number over varying connectivity between the nodes. Additionally, we explore the case of directed GP(N,k) and compare it with the undirected GP(N,k) results.

cond-mat.dis-nn↗

arXiv2023

Equilibrium via multi-spin-flip Glauber dynamics in Ising Model

Notwithstanding great strides that statistical mechanics has made in recent decades, an analytic solution of arguably the simplest model of relaxation dynamics, the Ising model in an applied external field remains elusive even in $1d$. Extant studies are based on numerics using single-spin-flip Glauber dynamics. There is no reason why this algorithm should lead to the global minimum energy state of the system. With this in mind, we explore multi-spin-flip parallel and sequential Glauber dynamics of Ising spins in $1d$ and also on a regular random graph of coordination number $z=3$. We view our study as a small initial step to test the generally implied hypothesis that the equilibrium is independent of the relaxational dynamics or if it carries some signature of it.

cond-mat.stat-mech↗

arXiv2020

Multifractality of correlated two-particle bound states in quasiperiodic chains

We consider the quasiperiodic Aubry-André chain in the insulating regime with localised single-particle states. Adding local interaction leads to the emergence of extended correlated two-particle bound states. We analyse the nature of these states including their multifractality properties. We use a projected Green function method to compute numerically participation numbers of eigenstates and analyse their dependence on the energy and the system size. We then perform a scaling analysis. We observe multifractality of correlated extended two-particle bound states, which we confirm independently through exact diagonalisation.

cond-mat.dis-nn↗

arXiv2019

Taming two interacting particles with disorder

We compute the scaling properties of the localization length $ξ_2$ of two interacting particles in a one-dimensional chain with diagonal disorder, and the connectivity properties of the Fock states. We analyze record large system sizes (up to $N=20000$) and disorder strengths (down to $W=0.5$). We vary the energy $E$ and the on-site interaction strength $u$. At a given disorder strength the largest enhancement of $ξ_2$ occurs for $u$ of the order of the single particle band width, and for two-particle states with energies at the center of the spectrum, $E=0$. We observe a crossover in the scaling of $ξ_2$ with the single particle localization length $ξ_1$ into the asymptotic regime for $ξ_1 > 100$ ($W < 1.0$). This happens due to the recovery of translational invariance and momentum conservation rules in the matrix elements of interconnected Fock eigenstates for $u=0$. The entrance into the asymptotic scaling is manifested through a nonlinear scaling function $ξ_2/ξ_1=F(uξ_1)$.

cond-mat.dis-nn↗

arXiv2019

Surprising variants of Cauchy's formula for mean chord length

We examine isotropic and anisotropic random walks which begin on the surface of linear ($N$), square ($N \times N$), or cubic ($N \times N \times N$) lattices and end upon encountering the surface again. The mean length of walks is equal to $N$ and the distribution of lengths $n$ generally scales as $n^{-1.5}$ for large $n$. Our results are interesting in the context of an old formula due to Cauchy that the mean length of a chord though a convex body of volume $V$ and surface $S$ is proportional to $V/S$. It has been realized in recent years that Cauchy's formula holds surprisingly even if chords are replaced by irregular insect paths or trajectories of colliding gas molecules. The random walk on a lattice offers a simple and transparent understanding of this result in comparison to other formulations based on Boltzmann's transport equation in continuum.

cond-mat.stat-mech↗

arXiv2019

Critical hysteresis on dilute triangular lattice

Critical hysteresis in the zero-temperature random-field Ising model on a two-dimensional triangular lattice has been studied earlier with site dilution on one sublattice. It was reported that criticality vanishes if less than one third of the sublattice is occupied. This appears at variance with recently obtained exact solutions of the model on dilute Bethe lattices and prompts us to revisit the problem using an alternate numerical method. Contrary to our speculation that criticality may not be exactly zero below one third dilution, the present study indicates it is nearly zero if approximately less than two-thirds of the sublattice is occupied. This suggests that hysteresis on dilute periodic lattices is qualitatively different from that on dilute Bethe lattices. Possible reasons are discussed briefly.

cond-mat.stat-mech↗

arXiv2017

Statistical Mechanics of Avalanches

Statistical mechanics of infinite avalanches is studied in the framework of nonequilibrium random-field Ising model. Critical behavior of the model on a random graph (dilute Bethe lattice) is analyzed in detail. We show that sites with a minimum coordination number 4 play a key role in the occurrence of infinite avalanches. Earlier results which did not seem to fit together very well are explained.

cond-mat.stat-mech↗

arXiv2015

Hysteresis in Random-field Ising model on a Bethe lattice with a mixed coordination number

We study zero-temperature hysteresis in the random-field Ising model on a Bethe lattice where a fraction $c$ of the sites have coordination number $z=4$ while the remaining fraction $1-c$ have $z=3$. Numerical simulations as well as probabilistic methods are used to show the existence of critical hysteresis for all values of $c > 0$. This extends earlier results for $c=0$ and $c=1$ to the entire range $0 \le c \le 1$, and provides new insight in non-equilibrium critical phenomena.

cond-mat.stat-mech↗

arXiv2015

Nonequilibrium random-field Ising model on a diluted triangular lattice

We study critical hysteresis in the random-field Ising model (RFIM) on a two-dimensional periodic lattice with a variable coordination number $z_{eff}$ in the range $3 \le z_{eff} \le 6$. We find that the model supports critical behavior in the range $4 < z_{eff} \le 6$, but the critical exponents are independent of $z_{eff}$. The result is discussed in the context of the universality of nonequilibrium critical phenomena and extant results in the field.

cond-mat.stat-mech↗

arXiv2013

Effect of Coordination Number on Nonequilibrium Critical Point

We study the nonequilibrium critical point of the zero temperature random field Ising model on a triangular lattice and compare it with known results on honeycomb, square, and simple cubic lattices. We suggest that the coordination number of the lattice rather than its dimension plays the key role in determining the universality class of the nonequilibrium critical behavior. This is discussed in the context of numerical evidence that equilibrium and nonequilibrium critical points of the zero-temperature random field Ising model belong to the same universality class. The physics of this curious result is not fully understood.

cond-mat.stat-mech↗