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Yeomans J.M. — Statistical Mechanics of Phase Transitions
Yeomans J.M. — Statistical Mechanics of Phase Transitions

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Название: Statistical Mechanics of Phase Transitions

Автор: Yeomans J.M.

Аннотация:

Recent developments have led to a good understanding of universality: why phase transitions in systems as diverse as magnets, fluids, liquid crystals, and superconductors can be brought under the same theoretical umbrella and accurately described by simple models. This book describes the physics underlying universality and then lays out the theoretical approaches now available for studying phase transitions. Traditional techniques, mean-field theory, series expansions, and the transfer matrix, are described; the Monte Carlo method is covered; and two chapters are devoted to the renormalization group which led to a breakthrough in the field. The book will be useful as a textbook for a course in phase transitions, as an introduction for graduate students undertaking research in related fields, and as an overview for scientists in other disciplines who work with phase transitions but who are not aware of the current tools of theoretical physics.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 153

Добавлена в каталог: 14.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha$      26 27 116
$\alpha$, mean-field theory      54 56
$\beta$      26 27 116
$\beta$, mean-field theory      53 56
$\Delta$      26 27 117
$\delta$, mean-field theory      54 57
$\epsilon$-expansion      140 ff.
$\eta$      20 26 27 117 121 136
$\eta$, mean-field theory      59
$\gamma$      26 27 117
$\gamma$, mean-field theory      54 57
$\nu$      26 27 117 135
$\nu$, mean-field theory      59
Antiferromagnet      5
Argon      1
Basin of attraction      115 135
Beta-brass      36 ff.
Binary alloy      6 36
Binary fluid      5 29
Block-spin transformation      13 ff. 136 139
Boltzmann weight      86
Boltzmann’s constant      15
boundary conditions      67 86
Boundary conditions, Monte Carlo      99
canonical ensemble      15
Cerium antimonide      4
chemical potential      39 137
Chiral clock model      49 75
Classical limit      45
Clock model      49
Coexistence curve      1
Complex eigenvalues of transfer matrix      75
Compressibility, exponent      27
Compressibility, isothermal      18
computer simulations      95 ff.
Concave function      19
Conformal group      120
Conformal invariance      120
Conjugate fields      108
Continuous phase transition      21
Convex function      19 22
Convexity of free energy      19
Cooperative behaviour      35
Corrections to scaling      26 32 89
Correlation function      20 ff.
Correlation function, and transfer matrix      70 ff.
Correlation function, exponents      26 27 117
Correlation function, one-dimensional Ising model      73
Correlation function, Ornstein — Zernike theory      57
Correlation function, power law decay      20
Correlation function, scaling behaviour      108 117
correlation length      10 20
Correlation length, and transfer matrix      70 ff.
Correlation length, at fixed point      108
Correlation length, exponent      26 27 117
Correlation length, one-dimensional Ising model      74
Correlation length, scaling behaviour      108 117
Critical isotherm exponent      26 27
Critical opalescence      13
Critical point      10 22
Critical point exponents      25 ff. 31
Critical point exponents, and conformal invariance      120
Critical point exponents, and scaling      115 ff.
Critical point exponents, definitions      26 27
Critical point exponents, equalities      116
Critical point exponents, inequalities      29
Critical point exponents, mean-field      53 5G
Critical point exponents, one-dimensional Ising model      130
Critical point exponents, table of values      46
Critical point exponents, universality of      27 45
Critical point of ferromagnet      1
Critical point of fluid      1
Critical point, behaviour of correlation function      20
Critical slowing down      100
Critical surface      111
Critical surface, example      113
Critical temperature      see “Critical point”
Crossover      47 112
Decimation, and Migdal — Kadanoff approximation      141
Decimation, and transfer matrix      141
Decimation, inconsistency of      135
Decimation, one-dimensional Ising model      125
Decimation, spin-1 Ising model      142
Decimation, two-dimensional Ising model      132
density      1
Detailed balance      96
Dilute Potts model      137
Disconnected diagrams      83
Disorder, substitutional      36
Disorder, topological      36
Duality      92
Eigenvalues of renormalization group      109
Eigenvalues of renormalization group, and critical exponents      115 ff.
Eigenvalues of renormalization group, example      115
Eigenvalues of transfer matrix and correlation length      72
Eigenvalues of transfer matrix, and free energy      69
Eigenvalues of transfer matrix, and partition function      68
Eigenvalues of transfer matrix, complex      75
Eigenvalues of transfer matrix, one-dimensional Ising model      72
Eigenvectors of renormalization group      110 ff.
Eigenvectors of transfer matrix and correlation function      72
Eigenvectors of transfer matrix, one-dimensional Ising model      72
Energy, internal      16 ff.
entropy      17 18 25
Europium sulphide      44
exchange interaction      8 35
Exponents      see “Critical point exponents”
Ferrimagnet      4 5
Ferroelectric      5
Ferromagnet      1 5 22
Ferromagnet, mean-field theory      50 ff.
Ferromagnet, phase-diagram      1 3 22
Field, magnetic      16
Field, scaled      118
Finite-size effects and Monte Carlo renormalization group      139
Finite-size effects in Monte Carlo simulation      99 102
First law of thermodynamics      16
First-order transition      1 3 21
Fixed point      108
Fixed point, example      113
Fixed point, Gaussian      140 144
Fixed point, Ising      140 144
Fixed point, one-dimensional Ising model      127
Flow diagram      110
Flow diagram, example      113
Flows, example      113
Flows, one-dimensional Ising model      127
Flows, renormalization group      108
Fluctuations      10 21
Fluid      1
Fluid, Monte Carlo simulations      103
Fluid, order parameter      1
Fluid, phase diagram      2
Fluid, thermodynamic variables      18
Free energy      16 ff. 22
Free energy, and high temperature series      83
Free energy, and renormalization group      107
Free energy, and trajectory sum      131
Free energy, and transfer matrix      69
Free energy, convexity      19
Free energy, ferromagnet      22
Free energy, Landau expansion      54 ff.
Free energy, mean-field      51
Free energy, one-dimensional Ising model      73 129 130
Free energy, scaling      116
Free energy, singular part      115
Gaussian fixed point      140
Generalized homogeneous function      116 121
Gibb’s free energy      22
Graphs, and high temperature series      81 ff.
Graphs, disconnected      83
Ground state      48
Guggenheim plot      27
Heisenberg model      43
Heisenberg model, three-dimensional exponents      46
Helmholtz free energy      see “Free energy”
High temperature series      80 ff.
Higher order transition      22
Hydrogen on iron      39 ff. 48
Hyperscaling relation      117
Importance sampling      96
Inequalities, critical exponents      29
Inequalities, Rushbrooke      29
INTERFACE      77 92
Internal energy      17 18
Irrelevant variable      110 116
Irrelevant variable, example      113
Ising fixed point      113 140
Ising lattice gas      49
Ising model      8 35
Ising model, equivalence to lattice gas      39
Ising model, mean-field theory      50 ff.
Ising model, one-dimensional, correlation function      73
Ising model, one-dimensional, correlation length      74
Ising model, one-dimensional, decimation transformation      124 ff.
Ising model, one-dimensional, exponents      129
Ising model, one-dimensional, free energy      73 129 130
Ising model, one-dimensional, high temperature series      86
Ising model, one-dimensional, low temperature series      88
Ising model, one-dimensional, magnetization      73
Ising model, one-dimensional, transfer matrix      67 ff.
Ising model, one-dimensional, zero-temperature phase transition      73 92
Ising model, spin-1      41 75 one-dimensional two-dimensional three-dimensional”)
Ising model, three-dimensional, and beta-brass      36 ff.
Ising model, three-dimensional, exponents      46
Ising model, three-dimensional, Monte Carlo      102
Ising model, three-dimensional, universality class      27 ff.
Ising model, two-dimensional      8 35
Ising model, two-dimensional, and hydrogen on iron      39
Ising model, two-dimensional, duality      92
Ising model, two-dimensional, exponents      30 46
Ising model, two-dimensional, high temperature series      80 ff.
Ising model, two-dimensional, low temperature series      86
Ising model, two-dimensional, magnetization      10
Ising model, two-dimensional, renormalization group      13 132
Krypton on graphite      41 ff.
Landau theory      54 ff.
Latent heat      1 22 25
Lattice gas      39
Lattice gas and hydrogen on iron      39
Lattice gas, Ising      49
Lattice types      33
Length scaling      10 107
Linear scaling fields      110 115
Linear scaling fields, example      113
Linked cluster theorem      83
Liquid crystal      5
Localized spins      44
Long-range order      13 20
Low temperature series      85 ff.
Low temperature series, one-dimensional Ising model      88
Low temperature series, Potts model      93
Low temperature series, two-dimensional Ising model      86
Magnesium fluoride      29 43
Magnet, thermodynamic variables for a      17
Magnet, uniaxial anisotropy in      29 (see also “Ferromagnet”)
Magnetic field      16
magnetization      4 17 22
Magnetization of ferromagnet      22
Magnetization of one-dimensional Ising model      73
Magnetization, exponent      26
Magnetization, fluctuations in      21
Magnetization, scaled      118
Magnetization, spontaneous      24
Magnetization, zero-field      24
Majority rule      14
Marginal variable      110
Markov chain      96 99
Maxwell — Boltzmarm statistics      16
Mean-field theory      50 ff.
Mean-field theory, classical      59
Mean-field theory, exponents      53 ff. 56
Mean-field theory, for correlation function      57
Mean-field theory, for Ising model      50 ff.
Mean-field theory, validity      61 (see also “Landau theory” “van “Weiss
Metropolis algorithm      96
Micelles      7
Migdal — Kadanoff transformation      141
Models      33 ff.
Models, antiferromagnetic spin-1/2 Ising      49
Models, chiral clock      49
Models, Heisenberg      43
Models, Ising lattice gas      49
Models, Ising with second neighbour interactions      76
Models, lattice gas      39
Models, p-state clock      49
Models, q-state Potts      41 49
Models, solid-on-solid      77
Models, spin-1 Ising      41 49
Models, spin-1/2 Ising      35 ff.
Models, X-Y      43
Momentum-space renormalization group      140 144
Monte Carlo      8 10 13 95
Monte Carlo renormalization group      139
Monte Carlo, accuracy      101
Monte Carlo, boundary conditions      99
Monte Carlo, choice of initial conditions      99
Monte Carlo, critical slowing down      100
Monte Carlo, finite-size effects      99 102
Monte Carlo, for fluids      103
Monte Carlo, for polymers      103
Monte Carlo, for three-dimensional Ising modei      102
Monte Carlo, influence of starting configuration      100
Monte Carlo, practical details      97
Monte Carlo, random numbers      100
Monte Carlo, statistical errors      101
Nobel prize      106
One-dimensional Ising model      see “Ising model one-dimensional”
Onsager      35
Opalescence, critical      13
Operators      108
Order parameter      1
Order parameter, exponent      26 27
Order parameter, ferromagnet      4
Order parameter, fluid      1
Order parameter, of beta-brass      36
Order parameter, scalar      29
Order parameter, symmetry of      27
Order-disorder transition      5 36
Pade approximant      92
Pair correlation function      see “Correlation function”
Paramagnet      31 35 73
Parameter space      108 113
Parameter space, example      113
Parameter space, size of for Potts model      137
Parameter space, truncation      134 139
Partition function      15 17 18
Partition function from high temperature series      83
Partition function from low temperature series      86
Partition function from transfer matrix      68
Perron — Frobenius theorem      70
phase diagram      1
Phase diagram, ferromagnet      1 22
Phase diagram, fluid      1
Phase diagram, two-dimensional Ising model      10
Phase separation      5 29
Phase space      95
Phase transition      1
Phase transition, continuous      1 22
Phase transition, critical      22
1 2
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