We present a simple lattice model showing a glassy behavior. $R$ matrix analysis predicts critical termination of the super-cooled fluid branch at density $ρ_g=0.1717$. This prediction is confirmed by dynamical numerical simulations, showing power-law divergences of relaxation time $τ_{1/2}$, as well as the 4-susceptibility $χ_4$ peak's location and height exactly at the predicted density. The power-law divergence of $χ_4$ continues up to $χ_4$ as high as $10^4$. Finite-size scaling study reveals divergence of correlation length accompanying the transition.
Building on the recently derived inhomogeneous mode-coupling theory, we extend the generalised mode-coupling theory of supercooled liquids to inhomogeneous environments. This provides a first-principles-based, systematic and rigorous way of deriving high-point dynamical susceptibilities from variations of the many-body dynamic structure factors with respect to their conjugate field. This new framework allows for a novel and fully microscopic possibility to probe for collective relaxation mechanisms in supercooled liquids near the mode-coupling glass transition.
Energy landscapes, ideal glasses, and their equation of state
利用Stillinger和Weber [Phys. Rev. A 25，978（1982）]最初提出的固有结构形式主义，我们概括了具有理想玻璃化转变的能量景观的热力学，并推导出其状态方程的结果。在这样做的过程中，我们确定了一个分离的结构和振动的贡献的压力，相应的模拟研究中进行的固有结构形式主义。我们开发了一个基本模型的景观适合简单的液体，这是基于软球势的标度特性的补充与平均场的吸引力。由此产生的状态方程提供了一个准确的表示模拟数据的Lennard-Jones流体，表明有用的基于水的配方的过冷液体热力学。最后，我们考虑的影响，一般理论和模型相对于所谓的Sastry密度和理想的玻璃化转变。我们的分析表明，定量之间的联系，可以作出的景观和模拟确定的Sastry密度的属性，它强调了理想的玻璃化转变和Kauzmann等熵条件之间的区别。
Key to resolving the scientific challenge of the glass transition is to understand the origin of the massive increase in viscosity of liquids cooled below their melting temperature (avoiding crystallisation). A number of competing and often mutually exclusive theoretical approaches have been advanced to describe this phenomenon. Some posit a bona fide thermodynamic phase to an "ideal glass", an amorphous state with exceptionally low entropy. Other approaches are built around the concept of the glass transition as a primarily dynamic phenomenon. These fundamentally different interpretations giv…
Thermodynamic Comparison and the Ideal Glass Transition of A Monatomic Systems Modeled as an Antiferromagnetic Ising Model on Husimi and Cubic Recursive Lattices of the Same Coordination Number
We propose an interacting lattice gas model of structural glass characterized by particle distinguishability and site-particle-dependent random nearest-neighboring particle interactions. This incorporates disorder quenched in the configuration space rather than in the physical space. The model exhibits non-trivial energetics while still admitting exact equilibrium states directly constructible at arbitrary temperature and density. The dynamics is defined by activated hopping following standard kinetic Monte Carlo approach without explicit facilitation rule. Kinetic simulations show emergent dy…
Expansion of the Gibbs potential for quantum many-body systems: General formalism with applications to the spin glass and the weakly non-ideal Bose gas
We use Monte Carlo (MC) methods to simulate a two-dimensional (2D) bond-diluted Ising model on the square lattice which has frustration between the nearest-neighbor interaction J1 and the next-nearest-neighbor interaction J2. In this paper, we use the parallel tempering algorithm to study the thermodynamics for different diluted ratio x and give the phase diagram. The presence of both frustration and disorder results in a spin-glass phase, which exists between the stripe antiferromagnetic phase and the Neel phase. We present the ground-state energy of T -> 0 and the size-dependence of Edwards-…
The understanding of thermodynamic glass transition has been hindered by the lack of proper models beyond mean-field theories. Here, we propose a three-dimensional lattice glass model on a simple cubic lattice that exhibits the typical dynamics observed in fragile supercooled liquids such as two-step relaxation, super-Arrhenius growth in the relaxation time, and dynamical heterogeneity. Using advanced Monte Carlo methods, we compute the thermodynamic properties deep inside the glassy temperature regime, well below the onset temperature of the slow dynamics. The specific heat has a finite jump …
It is presented a theory that describes a spin glass phase at finite temperatures in Kondo lattice systems with an additional RKKY interaction represented by long range, random couplings among localized spins like in the Sherrington- Kirkpatrick (SK) spin glass model. The problem is studied within the functional integral formalism where the spin operators are represented by bilinear combinations of fermionic (anticommuting) Grassmann variables. The Kondo and spin glass transitions are both described with the mean field like static ansatz that reproduces good results in the two well known limit…
In this study, the higher-order tensor renormalization group (HOTRG) method is applied to a lattice glass model that has local constraints on the occupation number of neighboring particles represented by many-body interactions. This model exhibits first- and second-order transitions depending on a certain model parameter. The results obtained by using the HOTRG method for the model were confirmed to be consistent with those obtained by a Markov-chain Monte Carlo (MCMC) method for systems of relatively small sizes. The transition points are accurately estimated by the HOTRG calculation for the …
Extended loop algorithm for pyrochlore Heisenberg spin models with spin-ice type degeneracy: application to spin-glass transition in antiferromagnets coupled to local lattice distortions
