On the Parisi-Toulouse hypothesis for the spin glass phase in mean-field theory

We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function $q(x)$ is computed at high orders in powers of $\tau=T_c-T$ and $H$. We find that none of the Parisi-Toulouse scaling hypotheses on the $q(x)$ behavior strictly holds, although some of them are violated only at high orders. The series is resummed yielding results in the whole spin-glass phase which are compared with those from a numerical evaluation of the $q(x)$. At the high order considered, the transition turns out to be third order on the Almeida-Thouless line, a result which is confirmed rigorously computing the expansion of the solution near the line at finite $\tau$. The transition becomes smoother for infinitesimally small field while it is third order at strictly zero field.Comment: 6 pages, 2 figure

Physics of the linear collider

This presentation intends to illustrate the specific capabilities of an e$^+$e$^-$ sub-TeV collider to provide answers on the basic issues in physics: origin of mass, hierarchy of masses, cosmological problems. Some foreseeable scenarios are discussed with a possible synergy with LHC.Comment: 20 pages, 16 figure

The Effects of Detector Descoping and Neutral Boson Mixing on New Gauge Boson Physics at the SSC

We examine how the abilities of an SDC-like detector to discover and identify the origin of a new neutral gauge boson are affected by $Z_1-Z_2$ mixing and by variations in detector parameters such as lepton pair mass resolution, particle identification efficiency, and rapidity coverage. Also examined is the sensitivity of these results to variations in structure function uncertainties and uncertainties in the machine integrated luminosity. Such considerations are of importance when dealing with the issues of detector descoping and design.Comment: 17 pages, 4 figures (available by request), phyzzx, ANL-HEP-PR-92-3