## 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 114

For #2 = 0 and a fixed coupling constant Ju point 1 represents the critical

temperature where K\ = K*. The designation K* indicates what is called a

constant K\ is ...

For #2 = 0 and a fixed coupling constant Ju point 1 represents the critical

temperature where K\ = K*. The designation K* indicates what is called a

**fixed****point**. Under RG transformation K; = RbK\ (3.90) so that at Tc the couplingconstant K\ is ...

Page 306

and the

be examined by considering a fluctuation x'n = xn — xc about each

The linear stability analysis can be done analytically. For the given fluctuation, Eq

.

and the

**fixed points**are at xc = 0, (a — I) /a. The stability of these**fixed points**canbe examined by considering a fluctuation x'n = xn — xc about each

**fixed point**.The linear stability analysis can be done analytically. For the given fluctuation, Eq

.

Page 307

In order to see the nature of the

point and follow successive iterations of this point, as shown in Figure 12.12fora

= 2.5,3.35, and 3.5; the dashed lines show successive iterations. Because xn+\ =

xn ...

In order to see the nature of the

**fixed points**, it is necessary to select an initialpoint and follow successive iterations of this point, as shown in Figure 12.12fora

= 2.5,3.35, and 3.5; the dashed lines show successive iterations. Because xn+\ =

xn ...

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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