We investigate the dynamical behaviour of the Ising model under a zero temperature quench with the initial fraction of up spins 0 ≤ x ≤ 1. In one dimension, the known results for persistence probability are verified; it shows algebraic decay for both up and down spins asymptotically with different exponents. It is found that the conventional finite size scaling is valid here. In two dimensions however, the persistence probabilities are no longer algebraic; in particular for x ≤ 0.5, persistence for the up (minority) spins shows the behaviour Pmin(t) ∼ t −γ exp(−(t/τ ) δ ) with time t, while for the down (majority) spins, Pmaj (t) approaches a finite value. We find that the timescale τ diverges as (xc − x) −λ , where xc = 0.5 and λ ≃ 2.31. The exponent γ varies as θ 2d + c0(xc − x) β where θ 2d ≃ 0.215 is very close to the persistence exponent in two dimensions; β ≃ 1. The results in two dimensions can be understood qualitatively by studying the exit probability, which for different system size is found to have the form E(x) = f ( x−xc xc )L 1/ν , with ν ≈ 1.47. This result suggests that τ ∼ Lz, wherez = λ ν = 1.57 ± 0.11 is an exponent not explored earlier.

We consider the zero temperature coarsening in the Ising model in two dimensions where the spins interact within the Moore neighbourhood. The Hamiltonian is given by H = − SiSj − κ SiS j ′ where the two terms are for the first neighbours and second neighbours respectively and κ ≥ 0. The freezing phenomena, already noted in two dimensions for κ = 0, is seen to be present for any κ. However, the frozen states show more complicated structure as κ is increased; e.g. local anti-ferromagnetic motifs can exist for κ > 2. Finite sized systems also show the existence of an iso-energetic active phase for κ > 2, which vanishes in the thermodynamic limit. The persistence probability shows universal behaviour for κ > 0, however it is clearly different from the κ = 0 results when non-homogeneous initial condition is considered. Exit probability shows universal behaviour for all κ ≥ 0. The results are compared with other models in two dimensions having interactions beyond the first neighbour.

We consider a single species reaction diffusion system on a two dimensional lattice where the particles A are biased to move towards their nearest neighbours and annihilate as they meet. Allowing the bias to take both negative and positive values parametrically, any nonzero bias is seen to drastically affect the behaviour of the system compared to the unbiased (simple diffusive) case. For positive bias, a finite number of dimers, which are isolated pairs of particles occurring as nearest neighbours, exist while for negative bias, a finite density of particles survives. Both the quantities vanish in a power law manner close to the diffusive limit with different exponents. The appearance of dimers is exclusively due to the parallel updating scheme used in the simulation. The results indicate the presence of a continuous phase transition at the diffusive point. In addition, a discontinuity is observed at the fully positive bias limit. The persistence behaviour is also analysed for the system.

We investigate the dynamics of classical spins mapped as walkers in a virtual "spin" space using a generalized two-parameter family of spin models characterized by parameters y and z [de Oliveira et al., J. Phys. A 26, 2317 (1993)JPHAC50305-447010.1088/0305-4470/26/10/006]. The behavior of S(x,t), the probability that the walker is at position x at time t, is studied in detail. In general S(x,t)∼t^{-α}f(x/t^{α}) with α≃1 or 0.5 at large times depending on the parameters. In particular, S(x,t) for the point y=1,z=0.5 corresponding to the Voter model shows a crossover in time; associated with this crossover, two timescales can be defined which vary with the system size L as L^{2}logL. We also show that as the Voter model point is approached from the disordered regions along different directions, the width of the Gaussian distribution S(x,t) diverges in a power law manner with different exponents. For the majority Voter case, the results indicate that the the virtual walk can detect the phase transition perhaps more efficiently compared to other nonequilibrium methods.

The formation of droplets of bio-molecular condensates through liquid-liquid phase separation (LLPS) of their component proteins is a key factor in the maintenance of cellular homeostasis. Different protein properties were shown to be important in LLPS onset, making it possible to develop predictors, which try to discriminate a positive set of proteins involved in LLPS against a negative set of proteins not involved in LLPS. On the other hand, the redundancy and multivalency of the interactions driving LLPS led to the suggestion that the large conformational entropy associated with non specific side-chain interactions is also a key factor in LLPS. In this work we build a LLPS predictor which combines the ability to form pi-pi interactions, with an unrelated feature, the propensity to stabilize the β-pairing interaction mode. The cross-β structure is formed in the amyloid aggregates, which are involved in degenerative diseases and may be the final thermodynamically stable state of protein condensates. Our results show that the combination of pi-pi and β-pairing propensity yields an improved performance. They also suggest that protein sequences are more likely to be involved in phase separation if the main chain conformational entropy of the β-pairing maintained droplet state is increased. This would stabilize the droplet state against the more ordered amyloid state. Interestingly, the entropic stabilization of the droplet state appears to proceed according to different mechanisms, depending on the fraction of “droplet-driving“ proteins present in the positive set.