Surface terms on the Nishimori line of the Gaussian Edwards-Anderson model

For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic boundary conditions and the adjacency pressure, i.e., the difference between the pressure of a box and the sum of the pressures of adjacent sub-boxes in which the box can been decomposed. We show that all those terms indeed behave proportionally to the surface size and prove the existence in the thermodynamic limit of the adjacency pressure.Comment: Final version with minor corrections. To appear in Journal of Statistical Physic

A Beautiful Life: Some Lessons for Legal Scholars

Book Revie

A mean-field monomer-dimer model with attractive interaction. The exact solution

A mean-field monomer-dimer model which includes an attractive interaction among both monomers and dimers is introduced and its exact solution rigorously derived. The Heilmann-Lieb method for the pure hard-core interacting case is used to compute upper and lower bounds for the pressure. The bounds are shown to coincide in the thermodynamic limit for a suitable choice of the monomer density m. The consistency equation characterising m is studied in the phase space (h, J), where h tunes the monomer potential and J the attractive potential. The critical point and exponents are computed and show that the model is in the mean-field ferromagnetic universality class.Comment: 32 pages, 6 figure

Spin Glass Computations and Ruelle's Probability Cascades

We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC formulation of the functional are developed. They are used to derive continuity and monotonicity properties of the functional retrieving a theorem of Guerra. We also detail the connection between the Aizenman-Sims-Starr variational principle and the Parisi formula. As a final application of the techniques, we rederive the Almeida-Thouless line in the spirit of Toninelli but relying on the RPC structure.Comment: 20 page

Immoral Promises

The proposition that “promises ought to be kept is one of the most important normative ideas or value judgements in our daily lives. But what about “illegal promises”? That is to say, what about promises that are, legally or morally speaking, malum in se or inherently wrongful, such as voluntary exchanges that are inherently immoral or wrongful, like bribes, blackmail, murder, etc.? In short, what moral obligations, if any, do such promises impose? Although many of the greatest thinkers in Western civilization have offered a wide variety of theories to explain the source of promissory obligations, it turns out there is a blind spot in this centuries-old conversation, for few theorists have given the problem of illegal or immoral promises any sustained thought. Nevertheless, illegal or immoral promises should be of theoretical interest to us because such promises may help us delimit the outer boundaries of promissory obligations