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Series

1984

Department of Physics Papers

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Articles 1 - 5 of 5

Full-Text Articles in Physics

Percolation In Dimensions D≥4, Joan Adler, Amnon Aharony, A. Brooks Harris Sep 1984

Percolation In Dimensions D≥4, Joan Adler, Amnon Aharony, A. Brooks Harris

Department of Physics Papers

In this paper we present extended mean cluster size series for the bond percolation problem for hypercubic lattices in d dimensions and analyze them for 4≤d≤9. Values of the critical exponent γ and the leading correction exponent Δ1 are deduced, and the Δ1 values for d>6 are compared with new analytic results.


Ε Expansion For The Conductivity Of A Random Resistor Network, A. Brooks Harris, Soobang Kim, Tom C. Lubensky Aug 1984

Ε Expansion For The Conductivity Of A Random Resistor Network, A. Brooks Harris, Soobang Kim, Tom C. Lubensky

Department of Physics Papers

We present a reanalysis of the renormalization-group calculation to first order in ε=6−d, where d is the spatial dimensionality, of the exponent, t, which describes the behavior of the conductivity of a percolating network at the percolation threshold. If we set t=(d−2)νp+ζ, where νp is the correlation-length exponent, then our result is ζ=1+(ε/42). This result clarifies several previously paradoxical results concerning resistor networks and shows that the Alexander-Orbach relation breaks down at order ε.


What Becomes Of Global Color, Philip C. Nelson, Sidney Coleman Apr 1984

What Becomes Of Global Color, Philip C. Nelson, Sidney Coleman

Department of Physics Papers

The recent demise of certain global unbroken symmetry generators in the presence of a grand unified magnetic monopole leads us to consider more carefully the notion of charges associated with gauge symmetries. It turns out that global transformations associated with the generators of the gauge group, and their charges, make sense only for extended systems which are sufficiently localized. GUT monopoles fail this criterion. Detailed consideration of the monopole-antimonopole system helps remove apparent paradoxes related to the chromodyon excitations of a single monopole and agrees with the previous result that some, but not all, of the states naively expected do ...


1/Σ Expansion For Quantum Percolation, A. Brooks Harris Mar 1984

1/Σ Expansion For Quantum Percolation, A. Brooks Harris

Department of Physics Papers

A method for obtaining a 1/σ expansion for certain statistical models is presented, where σ+1 is the coordination number of the lattice. The method depends on being able to generate exact recursion relations for the Cayley tree. By perturbing the recursion relation to take account of the dominant loops in a hypercubic lattice for large σ, we obtain corrections of order σ−2 to the recursion relations. For the tight-binding model on random bond clusters (the quantum-percolation problem) we obtain corrections to this order for the critical concentration p* at which the transition between localized and extended zero-energy ...


Hamiltonian Interpretation Of Anomalies, Philip C. Nelson, Luis Alvarez-Gaumé Jan 1984

Hamiltonian Interpretation Of Anomalies, Philip C. Nelson, Luis Alvarez-Gaumé

Department of Physics Papers

A family of quantum systems parametrized by the points of a compact space can realizeits classical symmetries via a new kind of nontrivial ray representation. We show that thisphenomenon in fact occurs for the quantum mechanics of fermions in the presence ofbackground gauge fields, and is responsible for both the nonabelian anomaly and Witten’sSU(2) anomaly. This provides a hamiltonian interpretation of anomalies: in the affectedtheories Gauss’ law cannot be implemented. The analysis clearly shows why there are nofurther obstructions corresponding to higher spheres in configuration space, in agreementwith a recent result of Atiyah and Singer.