Statistical Mechanics
Kinetics of thermal Mott transitions in the Hubbard model (1907.05880v1)
Gia-Wei Chern
2019-07-12
We present the first-ever microscopic dynamical simulation of the temperature-controlled Mott metal-insulator transition in the Hubbard model. By combining the efficient Gutzwiller method with molecular dynamics simulations, we demonstrate that the transformation from the correlated metal to the Mott insulator proceeds via the nucleation and growth of the Mott droplets. Moreover, the time evolution of the Mott volume fraction is found to follow a universal transformation kinetics. We show that after an initial incubation period, the early stage of the phase transformation is characterized by a constant nucleation rate and an interface-controlled cluster growth mechanism, consistent with the classical theory developed by Kolmogorov, Johnson, Mehl, and Avrami. This is followed by a novel intermediate stage of accelerated phase transformation that is significantly different from the prediction of the classical theory. Morevoer, the cluster-growth dynamics in this stage exhibits an unexpected avalanche behavior, similar to the Barkhausen noise in magnetization dynamics, even in the absence of quenched disorder. Detailed structural characterization further uncovers a universal correlation function for the transient mixed-phase states of the Mott transition. The implications of our findings for the recent nano-imaging experiments on metal-insulator transition of correlated materials are also discussed.
Nematic and gas-liquid transitions for sticky rods on square and cubic lattices (1905.05501v2)
P. Quiring, M. Klopotek, M. Oettel
2019-05-14
Using grand-canonical Monte Carlo simulations, we investigate the phase diagram of hard rods of length
with additional contact (sticky) attractions on square and cubic lattices. The phase diagram shows a competition between gas-liquid and ordering transitions (which are of demixing type on the square lattice for
and of nematic type on the cubic lattice for
). On the square lattice, increasing attractions initially lead to a stabilization of the isotropic phase. On the cubic lattice, the nematic transition remains of weak first order upon increasing the attractions. In the vicinity of the gas-liquid transition, the coexistence gap of the nematic transition quickly widens. These features are different from nematic transitions in the continuum.
Relevance of topological disorder on the directed percolation phase transition (1907.05809v1)
Manuel Schrauth, Jefferson S. E. Portela, Florian Goth
2019-07-12
Despite decades of research, the precise role of topological disorder in critical phenomena has yet to be fully understood. A major contribution has been the work by Barghathi and Vojta, which uses spatial correlations to explain puzzling earlier results. However, due to its reliance on coordination number fluctuations, their criterion cannot be applied to constant-coordination lattices, raising the question, for which classes of transitions can this type of disorder be a relevant perturbation? In order to cast light on this question, we investigate the non-equilibrium phase transition of the two-dimensional contact process on different types of spatial random graphs with varying or constant coordination number. Using large-scale numerical simulations, we find the disorder to be relevant, as the dynamical scaling behaviour turns out to be non-conventional, thus ruling out the directed percolation universality class. We conjecture that relevant topological disorders can be characterized by poor connectivity of the lattice. Based on that, we design two analysis tools that succeed in qualitatively distinguishing relevant from non-relevant topological disorders, supporting our conjecture and possibly pointing the way to a more complete relevance criterion.
Which wavenumbers determine the thermodynamic stability of soft matter quasicrystals? (1907.05805v1)
D. J. Ratliff, A. J. Archer, P. Subramanian, A. M. Rucklidge
2019-07-12
For soft matter to form quasicrystals an important ingredient is to have two characteristic lengthscales in the interparticle interactions. To be more precise, for stable quasicrystals, periodic modulations of the local density distribution with two particular wavenumbers should be favored, and the ratio of these wavenumbers should be close to certain special values. So, for simple models, the answer to the title question is that only these two ingredients are needed. However, for more realistic models, where in principle all wavenumbers can be involved, other wavenumbers are also important, specifically those of the second and higher reciprocal lattice vectors. We identify features in the particle pair interaction potentials which can suppress or encourage density modes with wavenumbers associated with one of the regular crystalline orderings that compete with quasicrystals, enabling either the enhancement or suppression of quasicrystals in a generic class of systems.
Critical Scaling and Aging near the Flux Line Depinning Transition (1907.05804v1)
Harshwardhan Chaturvedi, Ulrich Dobramysl, Michel Pleimling, Uwe C. Täuber
2019-07-12
We utilize Langevin molecular dynamics simulations to study dynamical critical behavior of magnetic flux lines near the depinning transition in type-II superconductors subject to randomly distributed attractive point defects. We employ a coarse-grained elastic line Hamiltonian for the mutually repulsive vortices and purely relaxational kinetics. In order to infer the stationary-state critical exponents for the continuous non-equilibrium depinning transition at zero temperature T = 0 and at the critical driving current density j_c, we explore two-parameter scaling laws for the flux lines' gyration radius and mean velocity as functions of the two relevant scaling fields T and j - j_c. We also investigate critical aging scaling for the two-time height auto-correlation function in the early-time non-equilibrium relaxation regime to independently measure critical exponents. We provide numerical exponent values for the distinct universality classes of non-interacting and repulsive vortices.
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