arXiv subjects

Dipanjan Mandal

Publications and source records attributed to Dipanjan Mandal.

15 recordsLinked to original sources

arXiv2026

Jamming states in random sequential adsorption of diffusion-limited aggregates

Motivated by the ubiquity of ramified fractal deposits in nature and engineered systems, we investigate the irreversible adsorption of diffusion-limited aggregation (DLA) clusters on a square lattice. We study the role of cluster shape diversity on jamming properties of the system by systematically controlling the number of distinct shapes used across and within realizations, encompassing both monodisperse and polydisperse model variants. Our large-scale simulations over a broad range of cluster sizes $2\leqslant k\leqslant4096$ show that the jamming density decreases with cluster size as a power-law $p_j(k)-p_j^\infty\sim k^{-α}$. Both $α$ and $p_j^\infty$ are found to depend on the degree of shape diversity, with $α$ ranging from $0.374(2)$ to $0.417(1)$. It is observed that increasing shape polydispersity promotes denser packing. Importantly, the fluctuations of the jamming density exhibit distinct scaling behavior: $σ(L)\sim1/L$ for a fixed pool of cluster shape(s), but remain $L$-independent when the pool of shape(s) is refreshed across different realizations. Furthermore, our results demonstrate that the differences between the model variants systematically diminish with increasing $k$ and are expected to vanish as $k\to\infty$ due to the statistical self-similarity of the DLA clusters.

cond-mat.stat-mech↗

arXiv2025

Low temperature nucleation rate calculations using the N-Fold way

We present a numerical study to determine nucleation rates for magnetisation reversal within the Ising model (lattice gas model) in the low-temperature regime, a domain less explored in previous research. To achieve this, we implemented the N-Fold way algorithm, a well-established method for low-temperature simulations, alongside a novel, highly efficient cluster identification algorithm. Our method can access nucleation rates up to 50 orders of magnitude lower than previously reported results. We examine three cases: homogeneous pure system, system with static impurities, and system with mobile impurities, where impurities are defined as sites with zero interactions with neighbouring spins (spin value of impurities is set to 0). Classical nucleation theory holds across the entire temperature range studied in the paper, for both the homogeneous system and the static impurity case. However, in the case of mobile impurities, the umbrella sampling technique seems ineffective at low mobility values. These findings provide valuable insights into nucleation phenomena at low temperatures, contributing to theoretical and experimental understanding.

cond-mat.stat-mech↗

arXiv2024

Mapping the influence of impurity interaction energy on nucleation in a lattice-gas model of solute precipitation

We study nucleation in the two dimensional Ising lattice-gas model of solute precipitation in the presence of randomly placed static and dynamic impurities. Impurity-solute and impurity-solvent interaction energies are varied whilst keeping other interaction energies fixed. In the case of static impurities, we observe a monotonic decrease in the nucleation rate when the difference between impurity-solute and impurity-solvent interaction energies is increased. The nucleation rate saturates to a minimum value with increasing interaction energy difference when the impurity density is low. However the nucleation rate does not saturate for high impurity densities. Similar behaviour is observed with dynamic impurities both at low and high densities. We explore a broad range of both symmetric and anti-symmetric interactions with impurities and map the regime for which the impurities act as a surfactant, decreasing the surface energy of the nucleating phase. We also characterise different nucleation regimes observed at different values of interaction energy. These include additional regimes where impurities play the role of inert-spectators, bulk-stabilizers or cluster together to create heterogeneous nucleation sites for solute clusters to form.

cond-mat.stat-mech↗

arXiv2023

Kinetic control of competing nuclei in a dimer lattice-gas model

Nucleation is a key step in the synthesis of new material from solution. Well-established lattice-gas models can be used to gain insight into the basic physics of nucleation pathways involving a single nucleus type. In many situations a solution is supersaturated with respect to more than one precipitating phase. This can generate a population both stable and metastable nuclei on similar timescales and hence complex nucleation pathways involving competition between the two. In this study we introduce a lattice-gas model based on two types of interacting dimer representing particles in solution. Each type of dimer nucleates to a specific space-filling structure. Our model is tuned such that stable and metastable phases nucleate on a similar timescale. Either structure may nucleate first, with probability sensitive to dimer mobility. We calculate these nucleation rates via Forward-Flux Sampling and demonstrate how the resulting data can be used to infer the nucleation outcome and pathway. Possibilities include direct nucleation of the stable phase, domination of long-lived metastable crystallites, and pathways in which the stable phase nucleates only after multiple post-critical nuclei of the metastable phase have appeared.

cond-mat.stat-mech↗

arXiv2022

Active Random Walks in One and Two Dimensions

We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the lattice in one and two dimensions, and derive exact results in the continuum limit. Next, we compute the large deviation free energy function in both one and two dimensions, which we use to compute the moments and the cumulants of the displacements exactly at late times. Our exact results demonstrate that the cross-correlations between the motion in the $x$ and $y$ directions in two dimensions persist in the large deviation function. We also demonstrate that the large deviation function of an active particle with diffusion displays two regimes, with differing diffusive behaviors. We verify our analytic results with kinetic Monte Carlo simulations of an active lattice walker in one and two dimensions.

cond-mat.stat-mech↗

arXiv2022

The freezing phase transition in hard core lattice gases on triangular lattice with exclusion up to seventh next-nearest neighbor

Hard core lattice gas models are minimal models to study entropy driven phase transitions. In the $k$-NN lattice gas, a particle excludes all sites upto the $k$-th next-nearest neighbors from being occupied by another particle. As $k$ increases from one, it extrapolates from nearest neighbor exclusion to the hard sphere gas. In this paper, we study the model on the triangular lattice for $k\leq 7$ using a flat histogram algorithm that includes cluster moves. Earlier studies had focused on $k\leq 3$. We show that for $4\leq k\leq 7$, the system undergoes a single phase transition from a low-density fluid phase to a high-density sublattice-ordered phase. Using partition function zeros and non-convexity properties of the entropy, we show that the transitions are discontinuous. The critical chemical potential, coexistence densities, and critical pressure are determined accurately.

cond-mat.stat-mech↗

arXiv2021

Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases

We introduce a rejection-free, flat histogram, cluster algorithm to determine the density of states of hard-core lattice gases. We show that the algorithm is able to efficiently sample low entropy states that are usually difficult to access, even when the excluded volume per particle is large. The algorithm is based on simultaneously evaporating all the particles in a strip and reoccupying these sites with a new appropriately chosen configuration. We implement the algorithm for the particular case of the hard-core lattice gas in which the first k next-nearest neighbors of a particle are excluded from being occupied. It is shown that the algorithm is able to reproduce the known results for k = 1,2,3 both on the square and cubic lattices. We also show that, in comparison, the corresponding flat histogram algorithms with either local moves or unbiased cluster moves are less accurate and do not converge as the system size increases.

cond-mat.stat-mech↗

arXiv2021

Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice: one or two phase transitions?

We obtain the phase diagram of the hard core lattice gas with third nearest neighbor exclusion on the triangular lattice using Monte Carlo simulations that are based on a rejection-free flat histogram algorithm. In a recent paper [J. Chem. Phys. 151, 104702 (2019)], it was claimed that the lattice gas with third nearest neighbor exclusion undergoes two phase transitions with increasing density, with the phase at intermediate densities exhibiting hexatic order with continuously varying exponents. Though a hexatic phase is expected when the exclusion range is large, it has not been seen earlier in hard core lattice gases with short range exclusion. In this paper, by numerically determining the entropies for all densities, we show unambiguously that there is only a single phase transition in the system between a low-density fluid phase and a high-density ordered sublattice phase, and that a hexatic phase is absent. The transition is shown to be first order in nature and the critical parameters are determined accurately.

cond-mat.stat-mech↗

arXiv2021

Nucleation rate in the two dimensional Ising model in the presence of random impurities

Nucleation phenomena are ubiquitous in nature and the presence of impurities in every real and experimental system is unavoidable. Yet numerical studies of nucleation are nearly always conducted for entirely pure systems. We have studied the behaviour of the droplet free energy in two dimensional Ising model in the presence of randomly positioned static and dynamic impurities. We have shown that both the free energy barrier height and critical nucleus size monotonically decreases with increasing the impurity density for the static case. We have compared the nucleation rates obtained from Classical Nucleation Theory and the Forward Flux Sampling method for different densities of the static impurities. The results show good agreement. In the case of dynamic impurities, we observe preferential occupancy the impurities at the boundary positions of the nucleus when the temperature is low. This further boosts enhancement of the nucleation rate due to lowering of the effective interfacial free energy.

cond-mat.stat-mech↗

arXiv2021

Breaking universality in random sequential adsorption on a square lattice with long-range correlated defects

Jamming and percolation transitions in the standard random sequential adsorption of particles on regular lattices are characterized by a universal set of critical exponents. The universality class is preserved even in the presence of randomly distributed defective sites that are forbidden for particle deposition. However, using large-scale Monte Carlo simulations by depositing dimers on the square lattice and employing finite-size scaling, we provide evidence that the system does not exhibit such well-known universal features when the defects have spatial long-range (power-law) correlations. The critical exponents $ν_j$ and $ν$ associated with the jamming and percolation transitions, respectively, are found to be non-universal for strong spatial correlations and approach systematically their own universal values as the correlation strength is decreased. More crucially, we have found a difference in the values of the percolation correlation length exponent $ν$ for a small but finite density of defects with strong spatial correlations. Furthermore, for a fixed defect density, it is found that the percolation threshold of the system, at which the largest cluster of absorbed dimers first establishes the global connectivity, gets reduced with increasing the strength of the spatial correlation.

cond-mat.stat-mech↗

arXiv2019

Phase diagram of a system of hard cubes on the cubic lattice

We study the phase diagram of a system of $2\times2\times2$ hard cubes on a three dimensional cubic lattice. Using Monte Carlo simulations, we show that the system exhibits four different phases as the density of cubes is increased: disordered, layered, sublattice ordered, and columnar ordered. In the layered phase, the system spontaneously breaks up into parallel slabs of size $2\times L \times L$ where only a very small fraction cubes do not lie wholly within a slab. Within each slab, the cubes are disordered; translation symmetry is thus broken along exactly one principal axis. In the solid-like sublattice ordered phase, the hard cubes preferentially occupy one of eight sublattices of the cubic lattice, breaking translational symmetry along all three principal directions. In the columnar phase, the system spontaneously breaks up into weakly interacting parallel columns of size $2\times 2\times L$ where only a very small fraction cubes do not lie wholly within a column. Within each column, the system is disordered, and thus translational symmetry is broken only along two principal directions. Using finite size scaling, we show that the disordered-layered phase transition is continuous, while the layered-sublattice and sublattice-columnar transitions are discontinuous. We construct a Landau theory written in terms of the layering and columnar order parameters, which is able to describe the different phases that are observed in the simulations and the order of the transitions. Additionally, our results near the disordered-layered transition are consistent with the $O(3)$ universality class perturbed by cubic anisotropy as predicted by the Landau theory.

cond-mat.stat-mech↗

arXiv2018

Non-Markovianity of qubit evolution under the action of spin environment

The question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the environment. If the environment is interacting with only one of the subsystems of a bipartite system, the dynamics of the entanglement in the bipartite system can be used to identify the direction of information flow. Here we study the dynamics of a two-level system interacting with an environment, which is also a heat bath, and consists of a large number of two-level quantum systems. Our model can be seen as a close approximation to the `spin bath' model at low temperatures. We analyze the Markovian nature of the dynamics, as we change the coupling between the system and the environment. We find the Kraus operators of the dynamics for certain classes of couplings. We show that any form of time-independent or time-polynomial coupling gives rise to non-Markovianity. Also, we witness non-Markovianity for certain parameter values of time-exponential coupling. Moreover, we study the transition from non-Markovian to Markovian dynamics as we change the value of coupling strength.

quant-ph↗

arXiv2017

Phase transitions in a system of hard $Y$-shaped particles on the triangular lattice

We study the different phases and the phase transitions in a system of $Y$-shaped particles, examples of which include Immunoglobulin-G and trinaphthylene molecules, on a triangular lattice interacting exclusively through excluded volume interactions. Each particle consists of a central site and three of its six nearest neighbours chosen alternately, such that there are two types of particles which are mirror images of each other. We study the equilibrium properties of the system using grand canonical Monte Carlo simulations that implements an algorithm with cluster moves that is able to equilibrate the system at densities close to full packing. We show that, with increasing density, the system undergoes two entropy-driven phase transitions with two broken-symmetry phases. At low densities, the system is in a disordered phase. As intermediate phases, there is a solid-like sublattice phase in which one type of particle is preferred over the other and the particles preferentially occupy one of four sublattices, thus breaking both particle-symmetry as well as translational invariance. At even higher densities, the phase is a columnar phase, where the particle-symmetry is restored, and the particles preferentially occupy even or odd rows along one of the three directions. This phase has translational order in only one direction, and breaks rotational invariance. From finite size scaling, we demonstrate that both the transitions are first order in nature. We also show that the simpler system with only one type of particles undergoes a single discontinuous phase transition from a disordered phase to a solid-like sublattice phase with increasing density of particles.

cond-mat.stat-mech↗

arXiv2017

The columnar-disorder phase boundary in a mixture of hard squares and dimers

A mixture of hard squares, dimers and vacancies on a square lattice is known to undergo a transition from a low-density disordered phase to high-density columnar ordered phase. Along the fully packed square-dimer line, the system undergoes an Kosterliz-Thouless type transition to a phase with power law correlations. We estimate the phase boundary separating the ordered and disordered phases by calculating the interfacial tension between two differently ordered phases within two different approximation schemes. The analytically obtained phase boundary is in good agreement with Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2017

Estimating the Critical Parameters of the Hard Square Lattice Gas Model

The hard square lattice gas model on a square lattice is known to undergo a continuous phase transition from a low density fluid-like phase to high density phase with columnar or smectic order. We estimate the critical activity $z_c$ by calculating, within an approximation scheme, the interfacial tension between two differently ordered columnar phases, and then setting it to zero. The approximation scheme allows for the ordered phases to have multiple defects and the interface between the ordered phases to have overhangs. We estimate $z_c=105.35$, which is in good agreement with existing Monte Carlo simulation results of $z_c \approx 97.5$, and is an improvement over earlier best estimates of $z_c=54.87$ and $z_c=135.63$.

cond-mat.stat-mech↗