## On the equation of state of an imperfect hard core gas |

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Page 4

CHAPTER 1 I SING MODEL OF FERROMAGNETISM la

As is well known, the

Weiss is based on the quantum mechanical exchange integral in the energy of ...

CHAPTER 1 I SING MODEL OF FERROMAGNETISM la

**Molecular Field Theory**As is well known, the

**molecular field theory**of ferromag- netism founded byWeiss is based on the quantum mechanical exchange integral in the energy of ...

Page 7

This is, of course, a direct result of using a molecular field which is constant at all

spin sites. If we now consider ... If the constant is chosen as v(0)/z and we let z

approach N then we obtain the

that ...

This is, of course, a direct result of using a molecular field which is constant at all

spin sites. If we now consider ... If the constant is chosen as v(0)/z and we let z

approach N then we obtain the

**molecular field theory**as before. This indicatesthat ...

Page 18

rather than R. Horwitz summed all chains and. rings (summation of chains in the

reducible expansion gives the

energy similar to the spherical model as given above, Horwitz' s results are

subject to ...

rather than R. Horwitz summed all chains and. rings (summation of chains in the

reducible expansion gives the

**molecular field theory**) and obtained the freeenergy similar to the spherical model as given above, Horwitz' s results are

subject to ...

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### Contents

THREE DIMENSIONAL LATTICE GAS | 21 |

THREE DIMENSIONAL HARD CORE GAS WITH | 39 |

CHAPTER k RESULTS OF THE THEORY OF THE REAL GAS | 52 |

3 other sections not shown

### Common terms and phrases

applied magnetic field base points Brout calculation canonical ensemble cluster expansion configuration Consequently critical temperature cross term Curie point Curie temperature curve defined Density Expansion derivation Diagrams Occuring diagrams of Figure dimensional Ising model dotted line bonds dotted line diagram dotted lines connected equivalent external dotted factor Figure A.l Figure B.2a fluctuations following diagrams Fourier transform free energy full semi-invariant Gaussian model given grand partition function hard core gas Horwitz Identical Diagrams internal dotted lines irreducible diagrams contribute irreducible graphs lattice gas Lennard-Jones Lennard-Jones potential logarithm loops Mayer model of ferromagnetism molecular field theory number of particles obtained overcounting phase transition Phys polynomial potential pressure real gas reducible combination Reducibly linked graphs renormalized represents result ring graphs saddle parameter solid lines spherical model graphs spin sum rule summation superposition approximation theorem theory of condensation three dimensional tion translational invariance vertex containing vertices zero applied magnetic