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Parongama Sen

Publications and source records attributed to Parongama Sen.

At least 109 records · Page 6Linked to original sources
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

Modulated Scale-free Network in the Euclidean Space

A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability proportional to $k_i \ell^α$. Our numerical study indicates that the network is Scale-free for all values of $α> α_c $ and the degree distribution decays stretched exponentially for the other values of $α$. The link length distribution follows a power law: $D(\ell) \sim \ell^δ$ where $δ$ is calculated exactly for the whole range of values of $α$.

cond-mat.stat-mech↗
arXiv2002

Phase transitions in a network with range dependent connection probability

We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-δ}$ in addition to nearest neighbour connections. This system has been shown to exhibit small world behaviour for $δ< 2$ above which its behaviour is like a regular lattice. From the study of the clustering coefficients, we show that there is a transition to a random network at $δ= 1$. The finite size scaling analysis of the clustering coefficients obtained from numerical simulations indicate that a continuous phase transition occurs at this point. Using these results, we find that the two transitions occurring in this network can be detected in any dimension by the behaviour of a single quantity, the average bond length. The phase transitions in all dimensions are non-trivial in nature.

cond-mat.stat-mech↗
arXiv2002

Persistence in an antiferromagnetic Ising model with conserved magnetisation

We obtain the persistence exponents for an antiferromagnetic Ising system in which the magnetisation is kept constant. This system belongs to Model C (system with non-conserved order parameter with a conserved density) and is expected to have persistence exponents different from that of Model A (system with no conservation) but independent of the conserved density. Our numerical results for both local persistence at zero temperature and global persistence at the critical temperature however indicate that the exponents are dependent on the conserved magnetisation in both two and three dimensions. This nonuniversal feature is attributed to the presence of the conserved field and is special to the persistence phenomena.

cond-mat.stat-mech↗
arXiv2002

Is there a true Model-D critical dynamics?

We show that non-locality in the conservation of both the order parameter and a noncritical density (model D dynamics) leads to new fixed points for critical dynamics. Depending upon the parameters characterizing the non-locality in the two fields, we find four regions: (i) model-A like where both the conservations are irrelevant (ii) model B-like with the conservation in the order parameter field relevant and the conservation in the coupling field irrelevant (iii) model C like where the conservation in the order parameter field is irrelevant but the conservation in the coupling field is relevant, and (iv) model D-like where both the conservations are relevant. While the first three behaviours are already known in dynamical critical phenomena, the last one is a novel phenomena due entirely to the non-locality in the two fields.

cond-mat.stat-mech↗
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↗
arXiv2001

Nature of largest cluster size distribution at the percolation threshold

Two distinct distribution functions $P_{sp}(m)$ and $P_{ns}(m)$ of the scaled largest cluster sizes $m$ are obtained at the percolation threshold by numerical simulations, depending on the condition whether the lattice is actually spanned or not. With $R(p_c)$ the spanning probability, the total distribution of the largest cluster is given by $P_{tot}(m) = R(p_c)P_{sp}(m) + (1-R(p_c))P_{ns}(m)$. The three distributions apparently have similar forms in three and four dimensions while in two dimensions, $P_{tot}(m)$ does not follow a familiar form. By studying the first and second cumulants of the distribution functions, the different behaviour of $P_{tot}(m)$ in different dimensions may be quantified.

cond-mat.dis-nn↗
arXiv2001

Small-world phenomena and the statistics of linear polymer networks

A regular lattice in which the sites can have long range connections at a distance l with a probabilty $P(l) \sim l^{-δ}$, in addition to the short range nearest neighbour connections, shows small-world behaviour for $0 \le δ< δ_c$. In the most appropriate physical example of such a system, namely the linear polymer network, the exponent $δ$ is related to the exponents of the corresponding n-vector model in the $n \to 0$ limit, and its value is less than $δ_c$. Still, the polymer networks do not show small-world behaviour. Here, we show that this is due a (small value) constraint on the number q of long range connections per monomer in the network. In the general $δ- q$ space, we obtain a phase boundary separating regions with and without small-world behaviour, and show that the polymer network falls marginally in the regular lattice region.

cond-mat.stat-mech↗
arXiv2001

Quantum fluctuation induced spatial stochastic resonance at zero temperature

We consider a model in which the quantum fluctuation can be controlled and show that the system responds to a spatially periodic external field at zero temperature. This signifies the occurrence of spatial stochastic resonance where the fluctuations are purely quantum in nature. Various features of the phenomenon are discussed.

cond-mat.stat-mech↗
arXiv2000

Quantum Phase Transitions in the Ising model in spatially modulated field

The phase transitions in the transverse field Ising model in a competing spatially modulated (periodic and oscillatory) longitudinal field are studied numerically. There is a multiphase point in absence of the transverse field where the degeneracy for a longitudinal field of wavelength $λ$ is $(\frac {1 + \sqrt{5}}{2})^{2N/λ}$ for a system with $N$ spins, an exact result obtained from the known result for $λ=2$. The phase transitions in the $Γ$ (transverse field) versus $h_0$ (amplitude of the longitudinal field) phase diagram are obtained from the vanishing of the mass gap $Δ$. We find that for all the phase transition points obtained in this way, $Δ$ shows finite size scaling behaviour signifying a continuous phase transition everywhere. The values of the critical exponents show that the model belongs to the universality class of the two dimensional Ising model. The longitudinal field is found to have the same scaling behaviour as that of the transverse field, which seems to be a unique feature for the competing field. The phase boundaries for two different wavelengths of the modulated field are obtained. Close to the multiphase point at $h_c$, the phase boundary behaves as $(h_c - h_0)^b$, where $b$ is also $λ$ dependent.

cond-mat.stat-mech↗
arXiv1999

On the universality of distribution of ranked cluster masses at critical percolation

The distribution of masses of clusters smaller than the infinite cluster is evaluated at the percolation threshold. The clusters are ranked according to their masses and the distribution $P(M/L^D,r)$ of the scaled masses M for any rank r shows a universal behaviour for different lattice sizes L (D is the fractal dimension). For different ranks however, there is a universal distribution function only in the large rank limit, i.e., $P(M/L^D,r)r^{-yζ} \sim g(Mr^y/L^D)$ (y and $ζ$ are defined in the text), where the universal scaling function g is found to be Gaussian in nature.

cond-mat.dis-nn↗
arXiv1999

Comparative study of spanning cluster distributions in different dimensions

The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions from two to five. The first two cumulants and the exponents for the universal scaling functions are shown to have simple power law variations with the dimensionality. The cases where multiple spanning clusters occur are discussed separately and compared.

cond-mat.stat-mech↗
arXiv1998

Non-local conservation in the coupling field: effect on critical dynamics

We consider the critical dynamics of a system with an $n$-component non-conserved order parameter coupled to a conserved field with long range diffusion. An exponent $σ$ characterizes the long range transport, $σ=2$ being the known locally conserved case. With renormalisation group calculations done upto one loop order, several regions are found with different values of the dynamic exponent $z$ in the $σ-n$ plane. For $n<4$, there are three regimes, I: nonuniversal, $σ$ dependent $z$, II: universal with $z$ depending on $n$ and III': conservation law irrelevant, $z$ being equal to that in the nonconserved case. The known locally conserved case belongs to regions I and II.

cond-mat.stat-mech↗
arXiv1998

Coexistence of spanning clusters in directed percolation

The probability distribution for the number of top to bottom spanning clusters in Directed percolation in two and three dimensions appears to be universal and is of the form $P(n) \sim \exp(-αn^2)$. We argue that $α$ is a new critical quantity vanishing at the upper critical dimension. The probability distribution of the individual masses of the spanning clusters is found to have a Pearson distribution with a lower cutoff. Various properties of the clusters are reported.

cond-mat.stat-mech↗
arXiv1997

Quantum Critical Behavior of the Infinite-range Transverse Ising Spin Glass : An Exact Numerical Diagonalization Study

We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field $Γ$ at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of $Γ$ and for system sizes $N \le 16$. We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of $Γ$. The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at $Γ_c \simeq 1.5$. Our estimates for the exponents at the transition are in agreement with those known from other approaches. For the dynamic exponent, we get $z=2.1 \pm 0.1$ which is in contradiction with a recent estimate ($z=4$). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for $Γ< Γ_c$.

cond-mat.stat-mech↗
arXiv1997

Probability distribution and sizes of spanning clusters at the percolation thresholds

For random percolation at p_c, the probability distribution P(n) of the number of spanning clusters (n) has been studied in large scale simulations. The results are compatible with $P(n) \sim \exp(-an^2)$ for all dimensions. We also study the variation of the average size (mass) of the spanning clusters when there are more than one spanning cluster. While the average size of the spanning clusters scales as usual with $L^D$ where $D = d- β/ν$ for any number of clusters, it shows a smooth decrease as the number of spanning clusters increases.

cond-mat.stat-mech↗
arXiv1997

Statistics of Red Sites on Elastic and Full Backbone

We investigate the number of red sites on the elastic and real backbone when right at the percolation threshold a spanning cluster exists between two sites at opposite faces of the lattice and found that it scales in the same way as in the case of percolation between two plates. We also find out that the number of common red sites scales similarly for both kinds of backbones for percolation between pairs of sites on opposite faces of the lattice. Our statistics for several quantities show that the the exponent for the elastic backbone approaches the one of the full backbone as dimensionality is increased.

cond-mat.stat-mech↗