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Somendra M. Bhattacharjee

Publications and source records attributed to Somendra M. Bhattacharjee.

68 records · Page 4Linked to original sources
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

Nonlocality in kinetic roughening

We propose a phenomenological equation to describe kinetic roughening of a growing surface in presence of long range interactions. The roughness of the evolving surface depends on the long range feature, and several distinct scenarios of phase transitions are possible. Experimental implications are discussed.

cond-mat.stat-mech↗
arXiv1997

On the Incommensurate Phase of Pure and Doped Spin-Peierls System CuGeO_3

Phases and phase transitions in pure and doped spin-Peierls system CuGeO_3 are considered on the basis of a Landau-theory. In particular we discuss the critical behaviour, the soliton width and the low temperature specific heat of the incommensurate phase. We show, that dilution leads always to the destruction of long range order in this phase, which is replaced by an algebraic decay of correlations if the disorder is weak.

cond-mat.dis-nn↗
arXiv1997

Dynamics of unbinding of polymers in a random medium

We have studied the aging effect on the dynamics of unbinding of a double stranded directed polymer in a random medium. By using the Monte Carlo dynamics of a lattice model in two dimensions, for which disorder is known to be relevant, the unbinding dynamics is studied by allowing the bound polymer to relax in the random medium for a waiting time and then allowing the two strands to unbind. The subsequent dynamics is formulated in terms of the overlap of the two strands and also the overlap of each polymer with the configuration at the start of the unbinding process. The interrelations between the two and the nature of the dependence on the waiting time are studied.

cond-mat.soft↗
arXiv1997

Deadlocks and waiting times in traffic jam

In a city of right moving and upmoving cars with hardcore constraint, traffic jam occurs in the form of bands. We show how the bands are destroyed by a small number of strictly left moving cars yielding a deadlock phase with a rough edge of left cars. We also show that the probability of waiting time at a signal for a particular tagged car has a power law dependence on time, indicating the absence of any characteristic time scale for an emergent traffic jam. The exponent is same for both the band and the deadlock cases. The significances of these results are discussed.

cond-mat.stat-mech↗
arXiv1996

Theory of tricriticality for miscut surfaces

We propose a theory for the observed tricriticality in the orientational phase diagram of Si(113) misoriented towards [001]. The systems seems to be at or close to a very special point for long range interactions.

cond-mat↗
arXiv1996

Infinite number of exponents for a spin glass transition

We consider the behavior of the overlap of $m (\geq 2)$ paths at the spin glass transition for a directed polymer in a random medium. We show that an infinite number of exponents is required to describe these overlaps. This is done in an $ε= d-2$ expansion without using the replica trick.

cond-mat↗
arXiv1996

Scaling of fluctuation for Directed polymers with random interaction

Using a finite size scaling form for reunion probability, we show numerically the existence of a binding-unbinding transition for Directed polymers with random interaction. The cases studied are (A1) two chains in 1+1 dimensions, (A2) two chains in 2+1 dimensions and (B) three chains in 1+1 dimensions. A similar finite size scaling form for fluctuation establishes a disorder induced transition with identical exponents for cases A2 and B. The length scale exponents in all the three cases are in agreement with previous exact renormalization group results.

cond-mat↗
arXiv1995

Fifty Years of the Exact Solution of the Two-Dimensional Ising Model by Onsager

The exact solution of the two-dimensional Ising model by Onsager in 1944 represents one of the landmarks in theoretical physics. On the occassion of the fifty years of the exact solution, we give a historical review of this model. After briefly discussing the exact solution by Onsager, we point out some of the recent developments in this field. The exact solution by Onsager has inspired several developments in various other fields. Some of these are also briefly mentioned.

cond-mat↗
arXiv1995

Protein Folding and Spin Glass

We explicitly show the connection between the protein folding problem and spin glass transition. This is then used to identify appropriate quantities that are required to describe the transition. A possible way of observing the spin glass transition is proposed.

cond-mat↗
arXiv1994

Finite Size Correction In A Disordered System - A New Divergence

We show that the amplitude of the finite size correction term for the $n$th moment of the partition function, for randomly interacting directed polymers, diverges (on the high temperature side) as $(n_c - n)^{-r}$, as a critical moment $n_c$ is approached. The exponent $r$ is independent of temperature but does depend on the effective dimensionality. There is no such divergence on the low temperature side ($n>n_c)$.

cond-mat↗
arXiv1993

Directed Polymers with Random Interaction : An Exactly Solvable Case -

We propose a model for two $(d+1)$-dimensional directed polymers subjected to a mutual $δ$-function interaction with a random coupling constant, and present an exact renormalization group study for this system. The exact $β$-function, evaluated through an $ε(=1-d)$ expansion for second and third moments of the partition function, exhibits the marginal relevance of the disorder at $d=1$, and the presence of a phase transition from a weak to strong disorder regime for $d>1$. The lengthscale exponent for the critical point is $ν=1/2\midε\mid$. We give details of the renormalization. We show that higher moments do not require any new interaction, and hence the $β$ function remains the same for all moments. The method is extended to multicritical systems involving an $m$ chain interaction. The corresponding disorder induced phase transition for $d>d_m=1/(m-1)$ has the critical exponent $ν_m=[2d(m-1)-2]^{-1}$. For both the cases, an essential singularity appears for the lengthscale right at the upper critical dimension $d_m$. We also discuss the strange behavior of an annealed system with more than two chains with pairwise random interactions among each other.

cond-mat↗
arXiv1993

Reunion of Vicious Walkers: Results from $ε$-Expansion -

The anomalous exponent, $η_{p}$, for the decay of the reunion probability of $p$ vicious walkers, each of length $N$, in $d$ $(=2-ε)$ dimensions, is shown to come from the multiplicative renormalization constant of a $p$ directed polymer partition function. Using renormalization group(RG) we evaluate $η_{p}$ to $O(ε^2)$. The survival probability exponent is $η_{p}/2$. For $p=2$, our RG is exact and $η_p$ stops at $O(ε)$. For $d=2$, the log corrections are also determined. The number of walkers that are sure to reunite is 2 and has no $ε$ expansion.

cond-mat↗