arXiv subjects

Subinay Dasgupta

Publications and source records attributed to Subinay Dasgupta.

28 records · Page 2Linked to original sources

arXiv2009

Phase of Ising spins on modular networks analogous to social polarization

Coordination processes in complex systems can be related to the problem of collective ordering in networks, many of which have modular organization. Investigating the order-disorder transition for Ising spins on modular random networks, corresponding to consensus formation in society, we observe two distinct phases: (i) ordering within each module at a critical temperature, followed by (ii) global ordering at a lower temperature. This indicates polarization of society into groups having contrary opinions can persist indefinitely even when mutual interactions between agents favor consensus.

cond-mat.stat-mech↗

arXiv2008

Multidimensional persistence behaviour in an Ising system

We consider a periodic Ising chain with nearest-neighbour and $r$-th neighbour interaction and quench it from infinite temperature to zero temperature. The persistence probability $P(t)$, measured as the probability that a spin remains unflipped upto time $t$, is studied by computer simulation for suitable values of $r$. We observe that as time progresses, $P(t)$ first decays as $t^{-0.22}$ (-the {\em first} regime), then the $P(t)-t$ curve has a small slope (in log-log scale) for some time (-the {\em second} regime) and at last it decays nearly as $t^{-3/8}$ (-the {\em third} regime). We argue that in the first regime, the persistence behaviour is the usual one for a two-dimensional system, in the second regime it is like that of a non-interacting (`zero-dimensional') system and in the third regime the persistence behaviour is like that of a one dimensional Ising model. We also provide explanations for such behaviour.

cond-mat.stat-mech↗

arXiv2007

Floating Phase in 2D ANNNI Model

We investigate whether the floating phase (where the correlation length is infinite and the spin-spin correlation decays algebraically with distance) exists in the temperature($T$) - frustration parameter ($κ$) phase diagram of 2D ANNNI model. To identify this phase, we look for the region where (i) finite size effect is prominent and (ii) some relevant physical quantity changes somewhat sharply and this change becomes sharper as the system size increases. For $κ< 0.5 $, the low temperature phase is ferromagnetic and we study energy and magnetization. For $κ> 0.5 $, the low temperature phase is antiphase and we study energy, layer magnetization, length of domain walls running along the direction of frustration, number of domain-intercepts that are of length 2 along the direction of frustration, and the number of domain walls that do not touch the upper and/or lower boundary. In agreement with some previous studies, our final conclusion is that, the floating phase exists, if at all, only along a line.

cond-mat.stat-mech↗

arXiv2007

Spin-spin Correlation in Some Excited States of Transverse Ising Model

We consider the transverse Ising model in one dimension with nearest-neighbour interaction and calculate exactly the longitudinal spin-spin correlation for a class of excited states. These states are known to play an important role in the perturbative treatment of one-dimensional transverse Ising model with frustrated second-neighbour interaction. To calculate the correlation, we follow the earlier procedure of Wu, use Szego's theorem and also use Fisher-Hartwig conjecture. The result is that the correlation decays algebraically with distance ($n$) as $1/\surd n$ and is oscillatory or non-oscillatory depending on the magnitude of the transverse field.

cond-mat.stat-mech↗

arXiv2007

Dynamics of unvisited sites in presence of mutually repulsive random walkers

We have considered the persistence of unvisited sites of a lattice, i.e., the probability $S(t)$ that a site remains unvisited till time $t$ in presence of mutually repulsive random walkers. The dynamics of this system has direct correspondence to that of the domain walls in a certain system of Ising spins where the number of domain walls become fixed following a zero termperature quench. Here we get the result that $S(t) \propto \exp(-αt^β)$ where $β$ is close to 0.5 and $α$ a function of the density of the walkers $ρ$. The number of persistent sites in presence of independent walkers of density $ρ^\prime$ is known to be $S^\prime (t) = \exp(-2 \sqrt{\frac{2}π} ρ^\prime t^{1/2})$. We show that a mapping of the interacting walkers' problem to the independent walkers' problem is possible with $ρ^\prime = ρ/(1-ρ)$ provided $ρ^\prime, ρ$ are small. We also discuss some other intricate results obtained in the interacting walkers' case.

cond-mat.stat-mech↗

arXiv2006

Floating Phase in 1D Transverse ANNNI Model

To study the ground state of ANNNI chain under transverse field as a function of frustration parameter $κ$ and field strength $Γ$, we present here two different perturbative analyses. In one, we consider the (known) ground state at $κ=0.5$ and $Γ=0$ as the unperturbed state and treat an increase of the field from 0 to $Γ$ coupled with an increase of $κ$ from 0.5 to $0.5+rΓ$ as perturbation. The first order perturbation correction to eigenvalue can be calculated exactly and we could conclude that there are only two phase transition lines emanating from the point $κ=0.5$, $Γ=0$. In the second perturbation scheme, we consider the number of domains of length 1 as the perturbation and obtain the zero-th order eigenfunction for the perturbed ground state. From the longitudinal spin-spin correlation, we conclude that floating phase exists for small values of transverse field over the entire region intermediate between the ferromagnetic phase and antiphase.

cond-mat.stat-mech↗

arXiv2006

A Small World Network of Prime Numbers

According to Goldbach conjecture, any even number can be broken up as the sum of two prime numbers : $n = p + q$. We construct a network where each node is a prime number and corresponding to every even number $n$, we put a link between the component primes $p$ and $q$. In most cases, an even number can be broken up in many ways, and then we chose {\em one} decomposition with a probability $|p - q|^α$. Through computation of average shortest distance and clustering coefficient, we conclude that for $α> -1.8$ the network is of small world type and for $α< -1.8$ it is of regular type. We also present a theoretical justification for such behaviour.

math.NT↗

arXiv2004

Persistence and dynamics in ANNNI chain

We investigate both the local and global persistence behaviour in ANNNI (axial next-nearest neighour Ising) model. We find that when the ratio $κ$ of the second neighbour interaction to the first neighbour interaction is less than 1, $P(t)$, the probability of a spin to remain in its original state upto time $t$ shows a stretched exponential decay. For $κ> 1$, $P(t)$ has a algebraic decay but the exponent is different from that of the nearest neighbour Ising model. The global persistence behaviour shows similar features. We also conduct some deeper investigations in the dynamics of the ANNNI model and conclude that it has a different dynamical behaviour compared to the nearest neighbour Ising model.

cond-mat.stat-mech↗

arXiv2002

Small-world properties of the Indian Railway network

Structural properties of the Indian Railway network is studied in the light of recent investigations of the scaling properties of different complex networks. Stations are considered as `nodes' and an arbitrary pair of stations is said to be connected by a `link' when at least one train stops at both stations. Rigorous analysis of the existing data shows that the Indian Railway network displays small-world properties. We define and estimate several other quantities associated with this network.

cond-mat.soft↗

arXiv2002

Short-time scaling in the critical dynamics of an antiferromagnetic Ising system with conserved magnetisation

We study by Monte Carlo simulations the short-time exponent $θ$ in an antiferromagnetic Ising system for which the magnetisation is conserved but the sublattice magnetisation (which is the order parameter in this case) is not. This system belongs to the dynamic class of model C. We use nearest neighbour Kawasaki dynamics so that the magnetisation is conserved {\em locally}. We find that in three dimensions $θ$ is independent of the conserved magnetisation. This is in agreement with the available theoretical studies, but in disagreement with previous simulation studies with global conservation algorithm. However, we agree with both these studies regarding the result $θ_C \ne θ_A$. We also find that in two dimensions, $θ_C = θ_A$.

cond-mat.stat-mech↗