Biomedical subjects

R Shrock

Publications and source records attributed to R Shrock.

10 recordsLinked to original sources

PubMed2001

Complex-temperature phase diagrams for the q-state Potts model on self-dual families of graphs and the nature of the q-->infinity limit.

Exact calculations of the Potts model partition function Z(G,q,v) have been presented for arbitrary q and temperature-like variable v on self-dual strip graphs G of the square lattice with fixed width L(y) and arbitrarily great length Lx with two types of boundary conditions. Letting Lx-->infinity, the resultant free energy and complex-temperature phase diagram have been computed, including the locus B where the free energy is nonanalytic. Results are analyzed for widths L(y)=1,2,3. These results have been used to study the approach to the large-q limit of B.

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PubMed2001

Exact T=0 partition functions for Potts antiferromagnets on sections of the simple cubic lattice.

We present exact solutions for the zero-temperature partition function of the q-state Potts antiferromagnet (equivalently, the chromatic polynomial P) on tube sections of the simple cubic lattice of fixed transverse size Lx x L(y) and arbitrarily great length L(z), for sizes Lx x L(y)=2 x 3 and 2 x 4 and boundary conditions (a) (FBC(x),FBC(y),FBC(z)) and (b) (PBC(x),FBC(y),FBC(z)), where FBC (PBC) denote free (periodic) boundary conditions. In the limit of infinite length, L(z)-->infinity, we calculate the resultant ground-state degeneracy per site W (=exponent of the ground-state entropy). Generalizing q from Z+ to C, we determine the analytic structure of W and the related singular locus Beta which is the continuous accumulation set of zeros of the chromatic polynomial. For the L(z)-->infinity limit of a given family of lattice sections, W is analytic for real q down to a value q(c). We determine the values of q(c) for the lattice sections considered and address the question of the value of q(c) for a d-dimensional Cartesian lattice. Analogous results are presented for a tube of arbitrarily great length whose transverse cross section is formed from the complete bipartite graph K(m,m).

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PubMed2001

Weak and electromagnetic nuclear decay signatures for neutrino reactions in Super-Kamiokande.

We suggest the study of events in the Super-Kamiokande neutrino data due to charged- and neutral-current neutrino reactions followed by weak and/or electromagnetic decays of struck nuclei and fragments thereof. This study could improve the prospects of obtaining evidence for tau production from nu(mu)-->nu(tau) oscillations and could augment the data sample used to disfavor nu(mu)-->nu(sterile) oscillations.

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PubMed2000

Ground-state entropy of the potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and W(q), the exponent of the ground-state entropy, for the q-state Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on square lattice strips, of width L(y)=3 and L(y)=4 vertices and arbitrarily great length Lx vertices, with both free and periodic boundary conditions. The resultant values of W for a range of physical q values are compared with each other and with the values for the full two-dimensional lattice. These results give insight into the effect of such nonnearest-neighbor couplings on the ground-state entropy. We show that the q=2 (Ising) and q=4 Potts antiferromagnets have zero-temperature critical points on the Lx-->infinity limits of the strips that we study. With the generalization of q from Z+ to C, we determine the analytic structure of W(q) in the q plane for the various cases.

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PubMed1999

Ground-state degeneracy of Potts antiferromagnets on two-dimensional lattices: approach using infinite cyclic strip graphs.

The q-state Potts antiferromagnet on a lattice Lambda exhibits nonzero ground-state entropy S0=kB ln W for sufficiently large q and hence is an exception to the third law of thermodynamics. An outstanding challenge has been the calculation of W(sq,q) on the square (sq) lattice. We present here an exact calculation of W on an infinite-length cyclic strip of the square lattice, which embodies the expected analytic properties of W(sq,q). Similar results are given for the kagomé lattice.

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PubMed1996