arXiv subjects

Sudip Mukherjee

Publications and source records attributed to Sudip Mukherjee.

31 records · Page 2Linked to original sources

arXiv2020

Dynamic scaling in the quenched disordered classical $N$-vector model

We revisit the effects of short-ranged random quenched disorder on the universal scaling properties of the classical $N$-vector model with cubic anisotropy. We set up the nonconserved relaxational dynamics of the model, and study the universal dynamic scaling near the second order phase transition. We extract the critical exponents and the dynamic exponent in a one-loop dynamic renormalisation group calculation with short-ranged isotropic disorder. We show that the dynamics near a critical point is generically slower when the quenched disorder is relevant than when it is not, independent of whether the pure model is isotropic or cubic anisotropic. We demonstrate the surprising thresholdless instability of the associated universality class due to perturbations from rotational invariance breaking quenched disorder-order parameter coupling, indicating breakdown of dynamic scaling. We speculate that this may imply a novel first order transition in the model, induced by a symmetry-breaking disorder.

cond-mat.stat-mech↗

arXiv2020

Long route to consensus: Two stage coarsening in a binary choice voting model

Formation of consensus, in binary yes/no type of voting, is a well defined process. However, even in presence of clear incentives, the dynamics involved can be incredibly complex. Specifically, formations of large groups of similarly opinionated individuals could create a condition of `support-bubbles' or spontaneous polarization that renders consensus virtually unattainable (e.g., the question of the UK exiting the EU). There have been earlier attempts in capturing the dynamics of consensus formation in societies through simple $Z_2$-symmetric models hoping to capture the essential dynamics of average behaviorof a large number of individuals in a statistical sense. However, in absence of external noise, they tend to reach a frozen state with fragmented and polarized states i.e., two or more groups of similarly opinionated groups with frozen dynamics. Here we show in a kinetic exchange opinion model (KEM) considered on $L \times L$ square lattices, that while such frozen states could be avoided, an exponentially slow approach to consensus is manifested. Specifically, the system could either reach consensus in a time that scales as $L^2$ or a long lived metastable state (termed a domain-wall state) for which formation of consensus takes a time scaling as $L^{3.6}$. The latter behavior is comparable to some voter-like models with intermediate states studied previously. The late-time anomaly in the time scale is reflected in the persistence probability of the model. Finally, the interval of zero-crossing of the average opinion i.e., the time interval over which the average opinion does not change sign is shown to follow a scale free distribution, which is compared with that seen in the opinion surveys regarding Brexit and associated issues in the last 40 years. The issue of minority spreading is also addressed by calculating the exit probability.

physics.soc-ph↗

arXiv2020

Econophysics Through Computation

We introduce here very briefly, through some selective choices of problems and through the sample computer simulation programs (following the request of the editor for this invited review in the Journal of Physics Through Computation), the newly developed field of econophysics. Though related attempts could be traced much earlier (see the Appendix), the formal researches in econophysics started in 1995. We hope, the readers (students \& researchers) can start themselves to enjoy the excitement, through the sample computer programs given, and eventually can undertake researches in the frontier problems, through the indicated survey literature provided.

physics.soc-ph↗

arXiv2019

Search of the ground state(s) of spin glasses and quantum annealing

We review our earlier studies on the order parameter distribution of the quantum Sherrington-Kirkpatrick (SK) model. Through Monte Carlo technique, we investigate the behavior of the order parameter distribution at finite temperatures. The zero temperature study of the spin glass order parameter distribution is made by the exact diagonalization method. We find in low-temperature (high-transverse-field) spin glass region, the tail (extended up to zero value of order parameter) and width of the order parameter distribution become zero in thermodynamic limit. Such observations clearly suggest the existence of a low-temperature (high-transverse-field) ergodic region. We also find in high-temperature (low-transverse-field) spin glass phase the order parameter distribution has nonzero value for all values of the order parameter even in infinite system size limit, which essentially indicates the nonergodic behavior of the system. We study the annealing dynamics by the paths which pass through both ergodic and nonergodic spin glass regions. We find the average annealing time becomes system size independent for the paths which pass through the quantum-fluctuation-dominated ergodic spin glass region. In contrast to that, the annealing time becomes strongly system size dependent for annealing down through the classical-fluctuation-dominated nonergodic spin glass region. We investigate the behavior of the spin autocorrelation in the spin glass phase. We observe that the decay rate of autocorrelation towards its equilibrium value is much faster in the ergodic region with respect to the nonergodic region of the spin glass phase.

cond-mat.stat-mech↗

arXiv2019

On the Question of Ergodicity in Quantum Spin Glass Phase and its role in Quantum Annealing

We first review, following our earlier studies, the critical behavior of the quantum Sherrington-Kirkpatrick (SK) model at finite as well as at zero temperatures. Through the analysis of the Binder cumulant we determined the entire phase diagram of the model and from the scaling analysis of the numerical data we obtained the correlation length exponent. For both the critical Binder cumulant and the correlation length exponent, we observed a crossover from classical- to quantum-fluctuation-dominated values at a finite temperature. We studied the behavior of the order parameter distribution of the model in the glass phase (at finite and zero temperatures). Along with a classical-fluctuation-dominated nonergodic region (where the replica symmetry is broken), we also found a quantum-fluctuation-dominated low-temperature ergodic region in the spin glass phase. In this quantum-fluctuation-dominated region, the order parameter distribution has a narrow peak around its most probable value, eventually becoming a delta function in the infinite-system-size limit (indicating replica symmetry restoration or ergodicity in the system). We also found that the annealing time (to reach a very low energy level of the classical SK model) becomes practically system-size-independent when the annealing paths pass through this ergodic region. In contrast, when such paths pass through the nonergodic region, the convergence time grows rapidly with the system size. We present a new study of the autocorrelation of the spins in both ergodic and nonergodic regions. We found a significant increase in the relaxation time (and also a change in the relaxation behavior) in the classical-fluctuation-dominated (nonergodic) region compared with that in the quantum-fluctuation-dominated (ergodic) region of the spin glass phase.

cond-mat.stat-mech↗

arXiv2018

Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain

We study the non-equilibrium evolution of concurrence of a Bell pair constituted of two qubits, through the measurement of Loschmidt echo (LE) under the scope of generalized central spin model. Having detected the Griffiths phase via derivative of LE in equilibrium, we show that in the non-equilibrium situation, the spin chain requires a temporal window to realize the effect of disorder. We show that within this timescale, LE falls off exponentially and this decay is maximally controlled by the initial states and coupling strength. Our detail investigation suggests that there actually exist three types of exponential decay, a Gaussian decay in ultra short time scale followed by two exponential decay in the intermediate time with two different decay exponents. The effect of the disorder starts appearing in the late time power law fall of LE where the power law exponent is strongly dependent on disorder strength and the final state but almost independent of initial states and coupling strength. This feature allows us to indicate the presence of Griffiths phase. To be precise, continuously varying critical exponent and wide distribution of relaxation time imprint their effect in LE in the late time limit where the power law fall is absent for quenching to a Griffiths phase. Here, LE vanishes following the fast exponential fall. Interestingly, for off-critical quenching LE attains a higher saturation value for increasing disorder strength, otherwise vanishes for a clean spin chain, referring to the fact that disorder prohibits the rapid decay of entanglement in long time limit. Moreover, we show that disorder is also able to destroy the light cone like nature of post quench quasi-particles as LE does not sense the singular time scales appearing for clean spin chain with qubits coupled at symmetric positions.

cond-mat.mes-hall↗

arXiv2018

Record breaking statistics near second order phase transitions

When a quantity reaches a value higher (or lower) than its value at any time before, it is said to have made a record. We numerically study the statistical properties of records in the time series of order parameters in different models near their critical points. Specifically, we choose transversely driven Edwards-Wilkinson model for interface depinning in (1+1) dimensions and the Ising model in two dimensions, as paradigmatic and simple examples of non-equilibrium and equilibrium critical behaviors respectively. The total number of record breaking events in the time series of the order parameters of the models show maxima when the system is near criticality. The number of record breaking events and associated quantities, such as the distribution of the waiting time between successive record events, show power law scaling near the critical point. The exponent values are specific to the universality classes of the respective models. Such behaviors near criticality can be used as a precursor to imminent criticality i.e. abrupt and catastrophic changes in the system. Due to the extreme nature of the records, its measurements are relatively free of detection errors and thus provide a clear signal regarding the state of the system in which they are measured.

cond-mat.stat-mech↗

arXiv2018

Possible Ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing

We explore the behavior of order parameter distribution of quantum Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo technique for the effective Suzuki-Trotter Hamil- tonian at finite temperatures and that at zero temperature obtained using exact diagonalization method. Our numerical results indicate the existence of low but finite temperature quantum fluc- tuation dominated ergodic region along with the classical fluctuation dominated high temperature nonergodic region in the spin glass phase of the model. In the ergodic region, the order parameter distribution gets narrower around the most probable value of the order parameter as the system size increases. In the other region, the Parisi order distribution function has non-vanishing value every- where in thermodynamic limit, indicating nonergodicity. We also show, that the average annealing time for convergence (to a low energy level of the model; within a small error range) becomes system size independent for annealing down through the (quantum fluctuation dominated) ergodic region. It becomes strongly system size dependent for annealing through the nonergodic region. Possible finite size scaling type behavior for the extent of the ergodic region is also addressed.

cond-mat.stat-mech↗

arXiv2018

Many body localization-delocalization transition in quantum Sherrington-Kirkpatrick model

We analyze many-body localization (MBL) to delocalization transition in Sherrington-Kirkpatrick (SK) model of Ising spin glass (SG) in the presence of a transverse field $Γ$. Based on energy resolved analysis, which is of relevance for a closed quantum system, we show that the quantum SK model has many-body mobility edges separating MBL phase which is non-ergodic and non-thermal from the delocalized phase which is ergodic and thermal. The range of the delocalized regime increases with increase in the strength of $Γ$ and eventually for $Γ$ larger than $Γ_{CP}$ the entire many-body spectrum is delocalized. We show that the Renyi entropy is almost independent of the system size in the MBL phase, hinting towards an area law in this infinite range model while the delocalized phase shows volume law scaling of Renyi entropy. We further obtain spin glass transition curve in energy density $ε$-$Γ$ plane from the collapse of eigenstate spin susceptibility. We demonstrate that in most of the parameter regime SG transition occurs close to the MBL transition indicating that the SG phase is non-ergodic and non-thermal while the paramagnetic phase is delocalized and thermal.

cond-mat.dis-nn↗

arXiv2016

Disorder induced phase transition in an opinion dynamics model: results in 2 and 3 dimensions

We study a model of continuous opinion dynamics with both positive and negative mutual interaction. The model shows a continuous phase transition between a phase with consensus (order) and a phase having no consensus (disorder). The mean field version of the model was already studied. Using extensive numerical simulations, we study the same model in $2$ and $3$ dimensions. The critical points of the phase transitions for various cases and the associated critical exponents have been estimated. The universality class of the phase transitions in the model is found to be same as Ising model in the respective dimensions.

cond-mat.stat-mech↗

arXiv2015

Classical-quantum crossover in the critical behavior of the transverse field S-K spin glass model

We study the critical behavior of Sherrington-Kirkpatrick model in transverse field (at finite temperature) using Monte Carlo simulation and exact diagonalization (at zero temperature). We determine the phase diagram of the model by estimating the Binder cumulant. We also determine the correlation length exponent from the collapse of the scaled data. Our numerical studies here indicate that critical Binder cumulant (indicating the universality class of the transition behavior) and the correlation length exponent cross over from their `classical' to `quantum' values at a finite temperature (unlike the cases of pure systems where such crossovers occur at zero temperature). We propose a qualitative argument supporting such an observation, employing a simple tunneling picture.

cond-mat.stat-mech↗

arXiv2014

Multivariable Optimization: Quantum Annealing & Computation

Recent developments in quantum annealing techniques have been indicating potential advantage of quantum annealing for solving NP-hard optimization problems. In this article we briefly indicate and discuss the beneficial features of quantum annealing techniques and compare them with those of simulated annealing techniques. We then briefly discuss the quantum annealing studies of some model spin glass and kinetically constrained systems.

cond-mat.stat-mech↗

arXiv2013

Quantum Annealing and Computation: A Brief Documentary Note

Major breakthrough in quantum computation has recently been achieved using quantum annealing to develop analog quantum computers instead of gate based computers. After a short introduction to quantum computation, we retrace very briefly the history of these developments and discuss the Indian researches in this connection and provide some interesting documents (in the Figs.) obtained from a chosen set of high impact papers (and also some recent news etc. blogs appearing in the Internet). This note is also designed to supplement an earlier note by Bose (Science and Culture, 79, pp. 337-378, 2013).

physics.hist-ph↗