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1983

Cleveland State University

Articles 1 - 3 of 3

Full-Text Articles in Physics

Convexity Of The Free Energy In Some Real-Space Renormalization-Group Approximations, Miron Kaufman, Robert B. Griffiths Oct 1983

Convexity Of The Free Energy In Some Real-Space Renormalization-Group Approximations, Miron Kaufman, Robert B. Griffiths

Miron Kaufman

Whereas the free energy for a spin system in a hierarchical lattice will be convex as a function of appropriate parameters (and thus the heat capacity positive, etc.), the same need not be true of a corresponding approximate real-space renormalization-group method applied to a Bravais lattice. Some examples are given which illustrate this point.

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Competing Criticality Of Short- And Infinite-Range Interactions On The Cayley Tree, Mehran Kardar, Miron Kaufman Sep 1983

Competing Criticality Of Short- And Infinite-Range Interactions On The Cayley Tree, Mehran Kardar, Miron Kaufman

Miron Kaufman

The Ising model, with equivalent-neighbor and nearest-neighbor interactions of Cayley tree connectivity, is solved exactly. Breaking translational symmetry by turning on the Cayley interactions is analogous to lowering spatial dimensionality in Bravais lattices. A range of classical criticality, a point of logarithmic corrections, a range of continuously varying power-law singularities, and a point of exponential singularity are successively encountered.

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Center-Of-Mass Properties Of Composite Systems Subject To Non-Linear External Interactions, James A. Lock Aug 1983

Center-Of-Mass Properties Of Composite Systems Subject To Non-Linear External Interactions, James A. Lock

Physics Faculty Publications

If two bound nonrelativistic quantum particles are each subject to a nonlinear external potential, their Schrödinger equation does not separate in relative and center-of-mass coordinates. For this case, the details of internal state of the composite affect its center-of-mass properties. The extent of this internal state influence is examined for an exactly soluble one-dimensional model system.

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