arXiv subjects

Harukuni Ikeda

Publications and source records attributed to Harukuni Ikeda.

42 records · Page 3Linked to original sources

arXiv2017

Mean field theory of the swap Monte Carlo algorithm

The swap Monte Carlo algorithm combines the translational motion with the exchange of particle species, and is unprecedentedly efficient for some models of glass former. In order to clarify the physics underlying this acceleration, we study the problem within the mean field replica liquid theory. We extend the Gaussian ansatz so as to take into account the exchange of particles of different species, and we calculate analytically the dynamical transition points corresponding to the swap and standard Monte Carlo algorithms. We show that the system evolved with the standard Monte Carlo algorithm exhibits the dynamical transition before that of the swap Monte Carlo algorithm. We also test the result by performing numerical simulations of a binary mixture of the Mari-Kurchan model, both with standard and swap Monte Carlo. This scenario provides a possible explanation for the efficiency of the swap Monte Carlo algorithm. Finally, we discuss how the thermodynamic theory of the glass transition should be modified based on our results.

cond-mat.dis-nn↗

arXiv2016

Note: A replica liquid theory of binary mixtures

It has been known that the binary replica liquid theory (RLT) is inconsistent with its one-component counterpart; In the limit that all atoms are identical, the configurational entropy and thus the glass transition point calculated by the binary RLT differ from those obtained by the one-component RLT. More specifically, an extra composition-dependent term, or the mixing entropy, remains finite in the configurational entropy computed by the binary RLT. In this Short Note, we reformulate the RLT in order to resolve this problem.

cond-mat.soft↗

arXiv2016

The Fredrickson-Andersen model with random pinning on Bethe lattices and its MCT transitions

We investigate the dynamics of the randomly pinned Fredrickson-Andersen model on the Bethe lattice. We find a line of random pinning dynamical transitions whose dynamical critical properties are in the same universality class of the $A_2$ and $A_3$ transitions of Mode Coupling Theory. The $A_3$ behavior appears at the terminal point, where the relaxation becomes logarithmic and the relaxation time diverges exponentially. We explain the critical behavior in terms of self-induced disorder and avalanches, strengthening the relationship discussed in recent works between glassy dynamics and Random Field Ising Model.

cond-mat.dis-nn↗

arXiv2016

The decoupling of the glass transitions in the two-component $p$-spin spherical model

Binary mixtures of large and small particles with disparate size ratio exhibit a rich phenomenology at their glass transition points. In order to gain insights on such systems, we introduce and study a two-component version of the $p$-spin spherical spin glass model. We employ the replica method to calculate the free energy and the phase diagram. We show that when the strengths of the interactions of each component are not widely separated, the model has only one glass phase characterized by the conventional one-step replica symmetry breaking. However when the strengths of the interactions are well separated, the model has three glass phases depending on temperature and component ratio. One is the "single" glass phase in which only the spins of one component are frozen while the spins of the other component remain mobile. This phase is characterized by the one-step replica symmetry breaking. The second is the "double" glass phase obtained by cooling further the single glass phase, in which the spins of the remaining mobile component are also frozen. This phase is characterized by the two-step replica symmetry breaking. The third is also the "double" glass phase, which however is formed by the simultaneous freezing of the spins of both components at the same temperatures and is characterized by the one-step replica symmetry breaking. We discuss the implications of these results for the glass transitions of binary mixtures.

cond-mat.dis-nn↗

arXiv2015

Fredrickson-Andersen model on Bethe lattice with random pinning

We study the effects of random pinning on the Fredrickson-Andersen model on the Bethe lattice. We find that the nonergodic transition temperature rises as the fraction of the pinned spins increases and the transition line terminates at a critical point. The freezing behavior of the spins is analogous to that of a randomly pinned p-spin mean-field spin glass model which has been recently reported. The diverging behavior of correlation lengths in the vicinity of the terminal critical point is found to be identical to the prediction of the inhomogeneous mode-coupling theory at the A3 singularity point for the glass transition.

cond-mat.dis-nn↗

arXiv2015

One-dimensional Kac model of dense amorphous hard spheres

We introduce a new model of hard spheres under confinement for the study of the glass and jamming transitions. The model is an one-dimensional chain of the $d$-dimensional boxes each of which contains the same number of hard spheres, and the particles in the boxes of the ends of the chain are quenched at their equilibrium positions. We focus on the infinite dimensional limit ($d \to \infty$) of the model and analytically compute the glass transition densities using the replica liquid theory. From the chain length dependence of the transition densities, we extract the characteristic length scales at the glass transition. The divergence of the lengths are characterized by the two exponents, $-1/4$ for the dynamical transition and $-1$ for the ideal glass transition, which are consistent with those of the $p$-spin mean-field spin glass model. We also show that the model is useful for the study of the growing length scale at the jamming transition.

cond-mat.soft↗