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Full-Text Articles in Physics
Convexity Of The Free Energy In Some Real-Space Renormalization-Group Approximations, Miron Kaufman, Robert B. Griffiths
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.
Competing Criticality Of Short- And Infinite-Range Interactions On The Cayley Tree, Mehran Kardar, Miron Kaufman
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.