Publications (2)0 Total impact
ABSTRACT: We consider the transverse dynamical structure factor of the anisotropic Heisenberg spin-1/2 chain (XXZ model) in the gapped antiferromagnetic regime ($\Delta > 1$). Specializing to the case of zero field, we use two independent approaches based on integrability (one valid for finite size, the other for the infinite lattice) to obtain the exact two-spinon part of this correlator. We discuss in particular its asymmetry with respect to the $\pi/2$ momentum line, its overall anisotropy dependence, and its contribution to sum rules. Comment: 19 pages, 6 figures
ABSTRACT: We study the competitive equilibrium of large random economies with linear activities using methods of statistical mechanics. We focus on economies with $C$ commodities, $N$ firms, each running a randomly drawn linear technology, and one consumer. We derive, in the limit $N,C\to\infty$ with $n=N/C$ fixed, a complete description of the statistical properties of typical equilibria. We find two regimes, which in the limit of efficient technologies are separated by a phase transition, and argue that endogenous technological change drives the economy close to the critical point.