arXiv subjects

Soumyajyoti Biswas

Publications and source records attributed to Soumyajyoti Biswas.

At least 19 recordsLinked to original sources

arXiv2026

Estimates of ground state energies for the quantum SK and 2D-EA models, using deGennes-Suzuki-Kubo mean-field annealing dynamics

We perform large scale quantum annealing of the Sherrington-Kirkpatrick (SK) spin glass up to a system size $N=40000$ to estimate its ground state energy using the deGennes-Suzuki-Kubo mean-field quantum Ising dynamics, extending the earlier results (reported in Eur. Phys. J. B {\bf 98}, 226 (2025)). Here we numerically solve the deGennes-Suzuki-Kubo annealing dynamics to obtain the spin configurations and subsequently the ground state energy for a given system size at the end of the annealing, starting from a quantum paramagnetic state. The method shows high efficiency, with an overall algorithmic cost of $O(N^3)$ in estimating the energy of the ground state. We later extend this quantum annealing study to estimate the ground state energies (starting again from the quantum paramagnetic phase, annealing down to any desired low value of the transverse field) for the Edwards-Anderson (EA) spin glass model on a square lattice.

cond-mat.dis-nn↗

arXiv2026

Models and Measures of Statistical Physics and Sociophysics for Fracture Mechanics and Earthquake Dynamics: An Introduction

The breaking or fracture of materials and damages or devastations due to earthquakes have caught our attention since the earliest stage of human civilization. In fact, at around 1500, Leonardo Da Vinci made the pioneering observation that, unlike elastic constants (formalized later by Hooke in 1678) of the materials, the tensile (breaking) strengths of nominally identical iron wires decrease drastically with their length, indicating the vanishing breaking strength of materials in the large size limit, suggesting the impossibility of constructing arbitrarily large structures. This was the first observation that unlike the elasticity of disordered materials, which remains defined in the thermodynamic limit (self averaging statistics), the breaking properties of the disordered materials have extreme (non self averaging) statistics. In spite of major and some precise developments in statistical physical modelling and characterizing the fracture mechanics (starting with Allan Griffith's crack nucleation theory in 1921 and the weakest link failure Fibre Bundle Model of Frederick Thomas Peirce in 1926) and of earthquake dynamics (starting with Robert Burridge and Leon Knopoff's continuum dynamical model in 1967 and later other discrete or lattice train models or fractal overlap models of stick slip earthquakes), no graduate level textbook in condensed matter physics or in statistical physics introduces the basic models and their properties. And now computer scientists and social scientists (coming with their social inequality measures applied to the avalanche statistics in precursor failures) are joining their efforts to explore the new precursory inequality measures for big avalanches or failures. This introductory review is designed to fill this gap with a view to introducing these to this wider audience and to take them to the current frontiers in these fields.

cond-mat.stat-mech↗

arXiv2026

Large earthquakes follow highly unequal ones

It was conjectured for a long time that the tectonic plates are in a self-organised state of criticality and that the Gutenberg-Richter law is a manifestation of that. It was recently shown that for a system near criticality, the inequality of their responses due to external driving would sharply rise and show universal behavior that could indicate the proximity of the system to a critical point. As a result, measures such as the Gini and Kolkata indices that quantify inequality can also serve as indicators of imminent criticality and those of diverging (system-spanning) responses. In the context of earthquakes, such a large response would correspond to events of high magnitudes. In this work, we show with numerical simulations and seismic data analysis that large earthquake events have a tendency to follow events that are highly unequal, similar to the case of a system near a critical point. Even though this is not a proof of tectonic plate systems being near-critical, a continuous monitoring of the inequality indices of the earthquake time series could be an useful tool for hazard estimates. We have applied this framework to models of earthquakes as well as to the earthquake time series from various seismically active regions, such as North America, Southern Japan, parts of Southeast Asia and Indonesia. The findings indicate that the SOC picture of tectonic plates is consistent with the increase in size inequality of earthquakes, even though this cannot be treated as a rigorous proof.

physics.geo-ph↗

arXiv2026

Subsampling of avalanches in the fiber bundle models of fracture

We study the subsampling of the avalanches in the fiber bundle model of fracture. In cases where only a part of the system is observed for the micro-failure events, the recorded avalanche statistics gets distorted compared to the actual fracture events. We show that, particularly in the cases where the load redistribution is localized, this distortion is significant. Surprisingly, however, near an elastic failure regime, the distortion is minimized, suggesting a much reduced observational capacity could still represent the actual failure dynamics in the case of fracture of elastic solids.

cond-mat.stat-mech↗

arXiv2026

Exponent spectrum of Lorenz curves and its relation to system's heterogeneity

We analyze the effect of microscopic heterogeneity on the Lorenz curve of macroscopic observables. Lorenz curve of a response function being a cumulative and bounded quantity, is often a more stable function than the corresponding probability density. We show here that by doing an exponent spectrum analysis of the complementary Lorenz curve, it is possible to obtain a reflection of the underlying heterogeneity that causes the response function to depart from a power law behavior. We demonstrate this framework first by synthetic data and then by analyzing the avalanche statistics of a two dimensional, Random Field Ising Model (RFIM) at zero temperature. This method can lead to possible use in estimating microscopic heterogeneity of a system from analysis of an estimated Lorenz curve, particularly in socio-economic and physical contexts where the full probability distribution function is unavailable.

physics.soc-ph↗

arXiv2026

Spin Glass Mapping of the Parallel Minority Game

The parallel minority game (PMG) extends the classical minority game to many choices, with each agent restricted to two predetermined alternatives. In this condition, minimizing the population variance across all choices is a complex combinatorial optimization problem. We show that this minimization is exactly equivalent to finding the ground state of an Ising spin glass in the mean-field limit, i.e., the Sherrington-Kirkpatrick model. By encoding the agent choices as spin variables, the variance becomes a quadratic Hamiltonian with quenched random couplings $J_{ij}$ and random fields $h_i$. This mapping reveals inherent frustration and connects the PMG to the well developed theory of spin glasses, providing a new perspective on the frozen, sub-optimal configurations observed in stochastic strategies.

cond-mat.dis-nn↗

arXiv2026

Local and global optimization in Parallel Minority Games

The Parallel Minority Game (PMG) refers to a set of Minority Games (MG), played in parallel, where each agent only has two choices to pick from, but each choice can host agents of many kind i.e., their other alternative can be from any other choices. While the pay-off function remains the same as that in the MG -- agents picking the less crowded of their two choices win positive pay-off -- the optimization of resource allocation is significantly harder in the PMG. While a global optimization demands a uniform population in all choices, a local optimization attempts to balance the population in the two choices for a given agent. In the MG these two objectives coincides, but generally in the PMG these are competing. We study several non-dictated, stochastic strategies and compare their efficiencies in attaining the local and global optimization objectives. Counterintuitively, a strategy with partial information of populations perform the best in terms of population fluctuation and overall payoff maximization.

physics.soc-ph↗

arXiv2026

Biswas-Chatterjee-Sen (BChS) kinetic exchange opinion model on modular networks

We study opinion formation in a society where agents interact on a modular network generated using a stochastic block model (SBM). Opinion dynamics is modeled through the Biswas-Chatterjee-Sen (BChS) kinetic exchange model, in which agents undergo pairwise interactions that could be positive or negative. By tuning the relative strength of intra- and inter-group connectivity inherent to the SBM, as well as the disagreement probability, we identify distinct collective phases. In particular, we observe a robust regime with strong intragroup ordering but no global consensus, in addition to fully ordered and disordered states. In the particular case of two modules, we observe an anti-ferromagnetic type ordering with the increase of negative interaction between the groups. We show approximate analytical calculations and numerical results of it. These results demonstrate how modular interaction structure can qualitatively alter collective opinion dynamics and hinder consensus formation.

physics.soc-ph↗

arXiv2026

Active-Absorbing Phase Transitions in the Parallel Minority Game

The Parallel Minority Game (PMG) is a synchronous adaptive multi-agent model that exhibits active-absorbing transitions characteristic of non-equilibrium statistical systems. We perform a comprehensive numerical study of the PMG under two families of microscopic decision rules: (i) agents update their choices based on instantaneous population in their alternative choices, and (ii) threshold-based activation that activates agents movement only after overcrowding density crossing a threshold. We measure time-dependent and steady state limits of activity $A(t)$, overcrowding fraction $F(t)$ as functions of the control parameter $g=N/D$, where $N$ is the number of agents and $D$ is the total number of sites. Instantaneous rules display mean-field directed-percolation (MF-DP) scaling with $β\approx1.00$, $δ\approx0.5$, and $ν_{\parallel}\approx2.0$. Threshold rules, however, produce a distinct non-mean-field universality class with $β\approx0.75$ and a systematic failure of dynamical scaling. We show that thresholding acts as a relevant perturbation to the critical behavior of the model. The results highlight how minimal cognitive features at the agent level fundamentally alter large-scale critical behavior in socio-economic and active systems.

cond-mat.stat-mech↗

arXiv2025

deGennes-Suzuki-Kubo Quantum Ising Mean Field Dynamics: Applications to Quantum Hysteresis, Heat Engines and Annealing

We briefly review the early development of the mean-field dynamics for cooperatively interacting quantum many-body systems, mapped to pseudo-spin (Ising-like) systems. We start with (Anderson, 1958) pseudo-spin mapping of the BCS (1957) Hamiltonian of superconductivity, reducing it to a mean-field Hamiltonian of XY (or effectively Ising) model in a transverse field. Then we get the mean-field estimate for the equilibrium gap in the ground state energy at different temperatures (gap disappearing at the transition temperature), which fits Landau's (1949) phenomenological theory of superfluidity. We then present in detail a general dynamical extension (for non-equilibrium cases) of the mean-field theory of quantum Ising systems (in a transverse field), following de Gennes' (1963) decomposition of the mean field into orthogonal classical cooperative (longitudinal) component and the quantum (transverse) component, with each component following Suzuki--Kubo (1968) mean-field dynamics. Next we discuss its applications to quantum hysteresis in Ising magnets (in presence of an oscillating transverse field), to quantum heat engines (employing transverse Ising model as working fluid), and to the quantum annealing of the Sherrington--Kirkpatrick (1975) spin glass by tuning down (to zero) the transverse field, which provides a very fast computational algorithm leading to ground state energy values converging to the best known analytic estimate for the model. Finally, we summarize the main results obtained and conclude about the effectiveness of the de Gennes--Suzuki--Kubo mean-field equations for the study of various dynamical aspects of quantum condensed matter systems.

cond-mat.stat-mech↗

arXiv2025

Quantum Annealing in SK Model Employing Suzuki-Kubo-deGennes Quantum Ising Mean Field Dynamics

We study a quantum annealing approach for estimating the ground state energy of the Sherrington-Kirpatrick mean field spin glass model using the Suzuki-Kubo-deGennes dynamics applied for individual local magnetization components. The solutions of the coupled differential equations, in discretized state, give a fast annealing algorithm (cost $N^3$) in estimating the ground state of the model: Classical ($E^0= -0.7629 \pm 0.0002$), Quantum ($E^0=-0.7623 \pm 0.0001$) and Mixed ($E^0=-0.7626 \pm 0.0001$), all of which are to be compared with the best known estimate $E^0= -0.763166726 \dots$ . We infer that the continuous nature of the magnetization variable used in the dynamics here is the reason for reaching close to the ground state quickly and also the reason for not observing the de-Almeida-Thouless line in this approach.

cond-mat.dis-nn↗

arXiv2025

Efficient strategy for Parallel Minority Games

We study the parallel Minority Game, where a group of agents, each having two choices, try to independently decide on a strategy such that they stay on minority between their own two choices. However, there are multiple such groups of agents, and some of them have common choices. This overlap brings in additional competition among the agents making the variance reduction a complex optimization problem. We study multiple stochastic strategies and find that the most efficient strategy is the one where the agents have just the memory of their last visit to the their alternative choice. The resulting dynamics, even though giving the lowest population variance among the strategies studied here, end up in a frozen state. However, the frozen state does not bring the the variance to its lowest possible value; a situation qualitatively analogous to spin-glass systems.

physics.soc-ph↗

arXiv2025

Order-disorder-order transitions and winning margins' scaling in kinetic exchange opinion model

The kinetic exchange opinion model shows a well-studied order disorder transition as the noise parameter, representing discord between interacting agents, is increased. A further increase in the noise drives the model, in low dimensions, to an extreme segregation ordering through a transition of similar nature. The scaling behavior of the winning margins have distinct features in the ordered and disordered phases that are similar to the observations noted recently in election data in various countries, explaining the qualitative differences in such scaling between tightly contested and land-slide election victories.

physics.soc-ph↗

arXiv2025

Classical Annealing of Sherrington-Kirkpatrick Spin Glass Using Suzuki-Kubo Mean-field Ising Dynamics

We propose and demonstrate numerically a fast classical annealing scheme for the Sherrington-Kirkpatrick (SK) spin glass model, employing the Suzuki-Kubo meanfield Ising dynamics (supplemented by a modified Thouless-Anderson-Palmer reaction field). The resultant dynamics, starting from any arbitrary paramagnetic phase (with local magnetizations $m_i=\pm 1$ for the $i^{th}$ spin, and the global magnetization $m=0$), takes the system quickly to an appropriate state with small local values of magnetization ($m_i$) commensurate with the (frustrated) interactions. As the temperature decreases with the annealing, the configuration practically remains (in an effective adiabatic way) close to a low energy configuration as the magnitudes of $m_i$'s and the spin glass order parameter $q$ grow to unity. While the configuration reached by the procedure is not the ground state, for an $N$-spin SK model (with $N$ up to 10000) the deviation in the energy per spin $E^0_N - E^0$ found by the annealing procedure scales as $N^{-2/3}$, with $E^0 = -0.7629\pm 0.0002$, suggesting that in the thermodynamic limit the energy per spin of the low energy configurations converges to the ground state of the SK model (analytical estimate being $E^0 =-0.7631667265 \dots$), fluctuation $σ_N $ in $E^0_N$ decreases as $\sim N^{-3/4}$ and the annealing time $τ_N \sim N$, making this protocol highly efficient in estimating the ground state of the SK model.

cond-mat.dis-nn↗

arXiv2025

Universal critical phase diagram using Gini index

The critical phase surface of a system, in general, can depend on one or more parameters. We show that by calculating the Gini index ($g$) of any suitably defined response function of a system, the critical phase surface can always be reduced to that of a single parameter, starting from $g=0$ and terminating at $g=g_f$, where $g_f$ is a universal number for a chosen response function in a given universality class. We demonstrate the construction with analytical and numerical calculations of mean field transverse field Ising model and site diluted Ising model on the Bethe lattice, respectively. Both models have two parameter critical phase surfaces -- transverse field and temperature for the first case and site dilution and temperature in the second case. Both can be reduced to single parameter transition points in terms of the Gini index. We have additionally demonstrated the validity of the method for a mean field two parameter opinion dynamics model that includes a tri-critical point. The method is generally applicable for any multi-parameter critical transition.

cond-mat.stat-mech↗

arXiv2025

Does Excellence Correspond to Universal Inequality Level?

We study the inequality of citations received for different publications of various researchers and Nobel laureates in Physics, Chemistry, Medicine and Economics using Google Scholar data from 2012 to 2024. Citation distributions are found to be highly unequal, with even greater disparity among Nobel laureates. Measures of inequality, such as the Gini and Kolkata indices, emerge as useful indicators for distinguishing Nobel laureates from others. Such high inequality corresponds to growing critical fluctuations, suggesting that excellence aligns with an imminent (self-organized dynamical) critical point. Additionally, Nobel laureates exhibit systematically lower values of the Tsallis--Pareto parameter $ b $ and Shannon entropy, indicating more structured citation distributions. We also analyze the inequality in Olympic medal tallies across countries and find similar levels of disparity. Our results suggest that inequality measures can serve as proxies for competitiveness and excellence.

physics.soc-ph↗

arXiv2024

Kinetic exchange opinion dynamics for the battleground-states in the 2024 US presidential elections

The strongly polarizing political discourse in the U. S. implies that a small minority of the population, determining the outcome of the presidential elections in a few so called battleground-states, also determines the outcome of the overall election. Given the almost equal distributions of the electoral college members in the so-called blue and red states, the members elected from these battleground states would determine the election results. We build a kinetic exchange opinion model that takes into account the dynamical nature of the opinions of the individuals in the battleground states and the already determined core voters of the non-battleground states. In a fully connected graph, we consider the interaction among the population in the battleground states while the agents in the non-battleground states are assumed to have fixed opinions. We provide the analytical results and numerical simulations using realistic parameters from the opinion poll of the previous election's data. Counter-intuitively, a more noisy environment predicts a higher chance of the Democrats' win.

physics.soc-ph↗

arXiv2024

Signature of maturity in cryptocurrency volatility

We study the fluctuations, particularly the inequality of fluctuations, in cryptocurrency prices over the last ten years. We calculate the inequality in the price fluctuations through different measures, such as the Gini and Kolkata indices, and also the $Q$ factor (given by the ratio between the highest value and the average value) of these fluctuations. We compare the results with the equivalent quantities in some of the more prominent national currencies and see that while the fluctuations (or inequalities in such fluctuations) for cryptocurrencies were initially significantly higher than national currencies, over time the fluctuation levels of cryptocurrencies tend towards the levels characteristic of national currencies. We also compare similar quantities for a few prominent stock prices.

physics.soc-ph↗