arXiv subjects

Soumyaditya Das

Publications and source records attributed to Soumyaditya Das.

9 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

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↗

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

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↗

arXiv2024

Finding critical points and correlation length exponents using finite size scaling of Gini index

The order parameter for a continuous transition shows diverging fluctuation near the critical point. Here we show, through numerical simulations and scaling arguments, that the inequality (or variability) between the values of an order parameter, measured near a critical point, is independent of the system size. Quantification of such variability through Gini index ($g$), therefore, leads to a scaling form $g=G\left[|F-F_c|N^{1/dν}\right]$, where $F$ denotes the driving parameter for the transition (e.g., temperature $T$ for ferromagnetic to paramagnetic transition transition, or lattice occupation probability $p$), $N$ is the system size, $d$ is the spatial dimension and $ν$ is the correlation length exponent. We demonstrate the scaling for the Ising model in two and three dimensions, site percolation on square lattice and the fiber bundle model of fracture.

cond-mat.stat-mech↗

arXiv2023

Critical scaling through Gini index

In the systems showing critical behavior, various response functions have a singularity at the critical point. Therefore, as the driving field is tuned towards its critical value, the response functions change drastically, typically diverging with universal critical exponents. In this work, we quantify the inequality of response functions with measures traditionally used in economics, namely by constructing a Lorenz curve and calculating the corresponding Gini index. The scaling of such a response function, when written in terms of the Gini index, shows singularity at a point that is at least as universal as the corresponding critical exponent. The critical scaling, therefore, becomes a single parameter fit, which is a considerable simplification from the usual form where the critical point and critical exponents are independent. We also show that another measure of inequality, the Kolkata index, crosses the Gini index at a point just prior to the critical point. Therefore, monitoring these two inequality indices for a system where the critical point is not known, can produce a precursory signal for the imminent criticality. This could be useful in many systems, including that in condensed matter, bio- and geophysics to atmospheric physics. The generality and numerical validity of the calculations are shown with the Monte Carlo simulations of the two dimensional Ising model, site percolation on square lattice and the fiber bundle model of fracture.

cond-mat.stat-mech↗