## Statistical mechanics: fundamentals and modern applicationsThis book examines the latest developments in statistical mechanics, a branch of physical chemistry and physics that uses statistical techniques to predict the properties and the behavior of chemical and physical systems. It begins with a review of some of the essential concepts and then discusses recent developments in both equilibrium and nonequilibrium statistical mechanics. It covers liquids, phase transitions, renormalization theory, Monte Carlo techniques, and chaos. |

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Page 108

In general, one of the directions dominates, and the exponents are those of the

Ising model! ... Only for d > 1 does it have a nonzero Tc. Universality says that the

critical behavior of a

In general, one of the directions dominates, and the exponents are those of the

Ising model! ... Only for d > 1 does it have a nonzero Tc. Universality says that the

critical behavior of a

**one**-**dimensional**Ising model and of a**one**-**dimensional**...Page 127

4.5 TAKAHASHI

Potential In this section, we shall use the exactly soluble

models to illustrate the ideas of the previous sections. Consider a line of length L

of rigid ...

4.5 TAKAHASHI

**ONE**-**DIMENSIONAL**FLUID MODELS 4.5.1 Hard-SpherePotential In this section, we shall use the exactly soluble

**one**-**dimensional**fluidmodels to illustrate the ideas of the previous sections. Consider a line of length L

of rigid ...

Page 325

To show this fractal nature, fractals and fractal dimension are first defined. The

fractal nature of many

Finally, the fractal dimension of Brownian motion and of polymers is discussed.

To show this fractal nature, fractals and fractal dimension are first defined. The

fractal nature of many

**one**-**dimensional**cellular automata is then demonstrated.Finally, the fractal dimension of Brownian motion and of polymers is discussed.

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### Contents

Classical Statistical Mechanics | 3 |

Quantum Statistical Mechanics | 45 |

Phase Transitions and Critical Phenomena | 83 |

Copyright | |

14 other sections not shown

### Common terms and phrases

attractor automata average behavior bifurcation Boltzmann Boltzmann equation Brownian motion Brownian particle BZ reaction calculate called canonical ensemble cell cellular automaton chaos Chapter coefficient collisions configuration consider coordinates correlation functions coupling constants critical exponents critical point defined depends derivation dimension discussed distribution function dynamics eigenvalues entropy equilibrium evaluated example ferromagnetic fixed point fluctuations fluid FORTRAN FORTRAN program fractal free energy frequency Gaussian Hamiltonian initial integral interactions Ising model iterations Kramers Langevin equation lattice limit cycle linear magnetization Markovian matrix method microcanonical ensemble microstates molecular nonequilibrium nonlinear number of particles obtained one-dimensional order parameter oscillations partition function Pathria phase space phase transition polymer potential power spectrum probability density problem protein quantities quantum mechanics RANDOM NUMBER random walk scaling Section shown in Figure simulation solution spin glass statistical mechanics steps stochastic temperature theorem thermodynamic limit total number values vector velocity zero