Frustrated Spin Model as a Hard-Sphere Liquid

We consider a frustrated spin model with a glassy dynamics characterized by a slow component and a fast component in the relaxation process. The slow process involves variables with critical behavior at finite temperature Tp and has a global character like the (structural) α-relaxation of glasses. The fast process has a more local character and can be associated to the β-relaxation of glasses. At temperature T > Tp the fast relaxation follows the non-Arrhenius behavior of the slow variables. At T ≲ Tp the fast variables have an Arrhenius behavior, resembling the α - β bifurcation of fragile glasses. The model allows us to analyze the relation between the dynamics and the thermodynamics.

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Hard-Sphere-like Dynamics in a Non-Hard-Sphere Liquid

Physical Review Letters ◽

10.1103/physrevlett.94.155301 ◽

2005 ◽

Vol 94 (15) ◽

Cited By ~ 35

Author(s):

T. Scopigno ◽

R. Di Leonardo ◽

L. Comez ◽

A. Q. R. Baron ◽

D. Fioretto ◽

...

Keyword(s):

Hard Sphere ◽

Hard Sphere Liquid

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Antiferromagnet-ferromagnet transition in the one-dimensional frustrated spin model

Physical Review B ◽

10.1103/physrevb.53.6435 ◽

1996 ◽

Vol 53 (10) ◽

pp. 6435-6441 ◽

Cited By ~ 27

Author(s):

V. Ya. Krivnov ◽

A. A. Ovchinnikov

Keyword(s):

Spin Model ◽

One Dimensional ◽

The One ◽

Frustrated Spin

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PHASE TRANSITION IN THE HEISENBERG FULLY-FRUSTRATED SIMPLE CUBIC LATTICE

Modern Physics Letters B ◽

10.1142/s0217984911026632 ◽

2011 ◽

Vol 25 (12n13) ◽

pp. 929-936 ◽

Cited By ~ 2

Author(s):

V. THANH NGO ◽

D. TIEN HOANG ◽

H. T. DIEP

Keyword(s):

Phase Transition ◽

Statistical Physics ◽

Spin Model ◽

Order Transition ◽

Heisenberg Spin ◽

Cubic Lattice ◽

Simple Cubic ◽

Simple Cubic Lattice ◽

Second Order Transition ◽

Frustrated Spin

The phase transition in frustrated spin systems is a fascinating subject in statistical physics. We show the result obtained by the Wang–Landau flat histogram Monte Carlo simulation on the phase transition in the fully frustrated simple cubic lattice with the Heisenberg spin model. The degeneracy of the ground state of this system is infinite with two continuous parameters. We find a clear first-order transition in contradiction with previous studies which have shown a second-order transition with unusual critical properties. The robustness of our calculations allows us to conclude this issue putting an end to the 20-year long uncertainty.

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Early Stage of Slow Dynamics in Dynamical Density Functional Theory of a Hard-Sphere Liquid near the Glass Transition

Journal of the Physical Society of Japan ◽

10.1143/jpsj.67.1505 ◽

1998 ◽

Vol 67 (5) ◽

pp. 1505-1508 ◽

Cited By ~ 11

Author(s):

Kazuhiro Fuchizaki ◽

Kyozi Kawasaki

Keyword(s):

Density Functional Theory ◽

Glass Transition ◽

Hard Sphere ◽

Density Functional ◽

Early Stage ◽

Slow Dynamics ◽

Functional Theory ◽

Hard Sphere Liquid

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Radial Distribution Function for a Hard Sphere Liquid: A Modified Percus-Yevick and Hypernetted-Chain Closure Relations

Journal of the Brazilian Chemical Society ◽

10.21577/0103-5053.20210117 ◽

2021 ◽

Author(s):

Felipe Carvalho ◽

João Pedro Braga

Keyword(s):

Distribution Function ◽

Radial Distribution Function ◽

Radial Distribution ◽

Hard Sphere ◽

Closure Relation ◽

Hard Sphere Liquid ◽

Hypernetted Chain ◽

Closure Relations ◽

Chain Approximation ◽

New Strategies

Establishment of the radial distribution function by solving the Ornstein-Zernike equation is still an important problem, even more than a hundred years after the original paper publication. New strategies and approximations are common in the literature. A crucial step in this process consists in defining a closure relation which retrieves correlation functions in agreement with experiments or molecular simulations. In this paper, the functional Taylor expansion, as proposed by J. K. Percus, is applied to introduce two new closure relations: one that modifies the Percus‑Yevick closure relation and another one modifying the Hypernetted-Chain approximation. These new approximations will be applied to a hard sphere system. An improvement for the radial distribution function is observed in both cases. For some densities a greater accuracy, by a factor of five times compared to the original approximations, was obtained.

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