Digital Commons Network^™

The Gamut: A Journal Of Ideas And Information, No. 13, Fall 1984, Cleveland State University

The Gamut Archives

CONTENTS OF ISSUE NO. 13, FALL 1984

Editorial: Our Fifth Year, 3

Dick Feagler: The Two Conventions, 4

Noted cynic observes the follies of national politics

The Gamut Photography Contest Winners, 9

Brenda L. Lewison, Jim Boland, Janine Bentivegna,

Eileen M. Delehanty, Genevieve Gauthier, Rhoda Grannum,

Buena Johnson, Charles J. Mintz, Tom Ritter, Wayne Sot

Louis Giannetti: Italian Neorealist Cinema, 20

Political philosophies and political realities shaped the work of the great post-war Italian filmmakers

Gary Engle: Krazy Kat and the Spirit of Surrealism, 28

George Herriman's famous cartoon strip reflects early twentieth century artistic ideas. …

Comment On Aproaches To The Tricritical Point In Quasibinary Liquid Mixtures, Miron Kaufman, Robert B. Griffiths

Miron Kaufman

No abstract provided.

Pseudodimensional Variation And Tricriticality Of Potts Models By Hierarchical Breaking Of Translational Invariance, Miron Kaufman, Mehran Kardar

Miron Kaufman

Potts models with equivalent- and nearest-neighbor interactions are solved exactly on Cayley trees. A parameter D is identified that plays a role similar to the spatial dimension on Bravais lattices. Breaking translational symmetry by the Cayley-tree hierarchy reduces D, leading to a changeover in the order of the phase transition via a novel tricritical point.

Spin Systems On Hierarchical Lattices. Ii. Some Examples Of Soluble Models, Miron Kaufman, Robert B. Griffiths

Miron Kaufman

Several examples are given of soluble models of phase-transition phenomena utilizing classical discrete spin systems with nearest-neighbor interaction on hierarchical lattices. These include critical exponents which depend continuously on a parameter, the Potts model on a lattice with two different coupling constants, surface tension, and excess free energy of a line of defects. In each case we point out similarities and differences with a corresponding Bravais-lattice model.

Duality And Potts Critical Amplitudes On A Class Of Hierarchical Lattices, Miron Kaufman

Miron Kaufman

By using the duality transformation on a class of hierarchical lattices, I show that the Potts critical amplitudes above and below the critical temperature are equal. Logarithmic modifications of the power-law singularity occur when the exponent 2—alpha is an even integer, but do not occur when 2—alpha equals an odd integer.

Short-Range And Infinite-Range Bond Percolation, Miron Kaufman, Mehran Kardar

Miron Kaufman

A method for generalizing bond-percolation problems to include the possibility of infinite-range (equivalent-neighbor) bonds is presented. On Bravais lattices the crossover from nonclassical to classical (mean-field) percolation criticality in the presence of such bonds is described. The Cayley tree with nearest-neighbor and equivalent-neighbor bonds is solved exactly, and a nonuniversal line of percolation transitions with exponents dependent on nearest-neighbor bond occupation probability is observed. Points of logarithmic and exponential singularity are also encountered, and the behavior is interpreted as dimensional reduction due to the breaking of translational invariance by bonds of Cayley-tree connectivity.

Critical Amplitude Of The Potts Model: Zeroes And Divergences, Miron Kaufman, David Andelman

Miron Kaufman

The critical amplitude of the q-state Potts-model free energy is studied as a function of q in two dimensions and on the diamond hierarchical lattice. The amplitude diverges at an infinite number of q values, qn,introducing logarithmic terms in the free energy. We expect that in each interval (qn,qn+1) there is a q value where the amplitude vanishes, affecting the singularity of the free energy as a function of temperature. Possible consequences for gelation and vulcanization of polymers are discussed.

Relativistic Invariance And Zitterbewegung, James A. Lock

Physics Faculty Publications

We examine the question of what it is about the structure of relativistic quantum mechanics that causes the nonintuitive phenomenon of the Zitterbewegung of particle position to exist. Further, we examine various assumptions concerning the measurement process which are implicit in the observation of Zitterbewegung.

Comment On Criticality Of The Anisotropic Quantum Heisenberg Model On A Self-Dual Hierarchical Lattice, Miron Kaufman, Mehran Kardar

Miron Kaufman

No abstract provided.

Realizable Renormalization Group And Finite-Size Scaling, Miron Kaufman, K. K. Mon

Miron Kaufman

We propose a sequence of renormalization-group transformations which are exact on hierarchical lattices and we argue, by employing finite-size scaling, that the corresponding sequence of critical exponents converges towards the exact values associated with a Bravais lattice. A test of this method is also presented.