Critical Slowing Down Exponents of Mode Coupling Theory

被引：40

作者：

Caltagirone, F. ^{[1
]}

Ferrari, U. ^{[1
,2
]}

Leuzzi, L. ^{[1
,2
]}

Parisi, G. ^{[1
,2
,3
]}

Ricci-Tersenghi, F. ^{[1
,2
,3
]}

Rizzo, T. ^{[1
,2
]}

机构：

[1] Univ Roma La Sapienza, Dip Fis, I-00185 Rome, Italy

[2] Univ Roma La Sapienza, UOS Roma Kerberos, IPCF CNR, I-00185 Rome, Italy

[3] Ist Nazl Fis Nucl, I-00185 Rome, Italy

来源：

PHYSICAL REVIEW LETTERS | 2012年 / 108卷 / 08期

关键词：

STRUCTURAL GLASS-TRANSITION; FINITE-SIZE CORRECTIONS; MEAN-FIELD THEORY; SPIN-GLASS; METASTABLE STATES; ORDER PARAMETERS; DYNAMICS; PHASE; RELAXATION; LIQUIDS;

D O I：

10.1103/PhysRevLett.108.085702

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A method is provided to compute the exponent parameter lambda yielding the dynamic exponents of critical slowing down in mode coupling theory. It is independent from the dynamic approach and based on the formulation of an effective static field theory. Expressions of lambda in terms of third order coefficients of the action expansion or, equivalently, in terms of six point cumulants are provided. Applications are reported to a number of mean-field models: with hard and soft variables and both fully connected and dilute interactions. Comparisons with existing results for the Potts glass model, the random orthogonal model, hard and soft-spin Sherrington-Kirkpatrick, and p-spin models are presented.

引用

页数：5

共 51 条

[1] Mode coupling as a Landau theory of the glass transition [J].

Andreanov, A. ;

Biroli, G. ;

Bouchaud, J. -P. .

EPL, 2009, 88 (01)

[2] DYNAMICS OF SUPERCOOLED LIQUIDS AND THE GLASS-TRANSITION [J].

BENGTZELIUS, U ;

GOTZE, W ;

SJOLANDER, A .

JOURNAL OF PHYSICS C-SOLID STATE PHYSICS, 1984, 17 (33) :5915-5934

[3] Mode-coupling approximations, glass theory and disordered systems [J].

Bouchaud, JP ;

Cugliandolo, L ;

Kurchan, J ;

Mezard, M .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 1996, 226 (3-4) :243-273

[4] Ergodicity breaking in a mean field Potts glass: A Monte Carlo investigation [J].

Brangian, C ;

Kob, W ;

Binder, K .

COMPUTER PHYSICS COMMUNICATIONS, 2002, 147 (1-2) :154-157

[5] Finite-size scaling at the dynamical transition of the mean-field 10-state Potts glass [J].

Brangian, C ;

Kob, W ;

Binder, K .

EUROPHYSICS LETTERS, 2001, 53 (06) :756-761

[6]

Caltagirone F., IN PRESS

[7] Renormalization Group Analysis of the Random First-Order Transition [J].

Cammarota, Chiara ;

Biroli, Giulio ;

Tarzia, Marco ;

Tarjus, Gilles .

PHYSICAL REVIEW LETTERS, 2011, 106 (11)

[8] BETHE LATTICE SPIN-GLASS - THE EFFECTS OF A FERROMAGNETIC BIAS AND EXTERNAL FIELDS .2. MAGNETIZED SPIN-GLASS PHASE AND THE DE ALMEIDA-THOULESS LINE [J].

CARLSON, JM ;

CHAYES, JT ;

SETHNA, JP ;

THOULESS, DJ .

JOURNAL OF STATISTICAL PHYSICS, 1990, 61 (5-6) :1069-1084

[9] Spin-glass theory for pedestrians [J].

Castellani, T ;

Cavagna, A .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2005, :215-266

[10] Role of the interaction matrix in mean-field spin glass models -: art. no. 046112 [J].

Cherrier, R ;

Dean, DS ;

Lefèvre, A .

PHYSICAL REVIEW E, 2003, 67 (04) :10-461121

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