Spectral properties of a partially spin-polarized one-dimensional Hubbard/Luttinger superfluid

We calculate the excitation spectra of a spin-polarized Hubbard chain away from half-filling, using a high-precision momentum-resolved time-dependent Density Matrix Renormalization Group method. Focusing on the U<0 case, we present in some detail the single-fermion, pair, density and spin spectra, and discuss how spin-charge separation is altered for this system. The pair spectra show a quasi-condensate at a nonzero momentum proportional to the polarization, as expected for this Fulde-Ferrel-Larkin-Ovchinnikov-like superfluid.Comment: 4 pages, 3 low resolution color fig

Towards a statistical theory of transport by strongly-interacting lattice fermions

We present a study of electric transport at high temperature in a model of strongly interacting spinless fermions without disorder. We use exact diagonalization to study the statistics of the energy eigenvalues, eigenstates, and the matrix elements of the current. These suggest that our nonrandom Hamiltonian behaves like a member of a certain ensemble of Gaussian random matrices. We calculate the conductivity $\sigma(\omega)$ and examine its behavior, both in finite size samples and as extrapolated to the thermodynamic limit. We find that $\sigma(\omega)$ has a prominent non-divergent singularity at $\omega=0$ reflecting a power-law long-time tail in the current autocorrelation function that arises from nonlinear couplings between the long-wavelength diffusive modes of the energy and particle number

Critical behavior of a three-dimensional dimer model

The phase transition behavior of a dimer model on a three-dimensional lattice is studied. This model is of biological interest because of its relevance to the lipid bilayer main phase transition. The model has the same kind of inactive low-temperature behavior as the exactly solvable Kasteleyn dimer model on a two-dimensional honeycomb lattice. Because of low-temperature inactivity, determination of the lowest-lying excited states allows one to locate the critical temperature. In this paper the second-lowest-lying excited states are studied and exact asymptotic results are obtained in the limit of large lattices. These results together with a finite-size scaling ansatz suggest a logarithmic divergence of the specific heat aboveT c for the three-dimensional model. Use of the same ansatz recovers the exact divergence (α=½) for the two-dimensional model

Vicious Walkers in a Potential

We consider N vicious walkers moving in one dimension in a one-body potential v(x). Using the backward Fokker-Planck equation we derive exact results for the asymptotic form of the survival probability Q(x,t) of vicious walkers initially located at (x_1,...,x_N) = x, when v(x) is an arbitrary attractive potential. Explicit results are given for a square-well potential with absorbing or reflecting boundary conditions at the walls, and for a harmonic potential with an absorbing or reflecting boundary at the origin and the walkers starting on the positive half line. By mapping the problem of N vicious walkers in zero potential onto the harmonic potential problem, we rederive the results of Fisher [J. Stat. Phys. 34, 667 (1984)] and Krattenthaler et al. [J. Phys. A 33}, 8835 (2000)] respectively for vicious walkers on an infinite line and on a semi-infinite line with an absorbing wall at the origin. This mapping also gives a new result for vicious walkers on a semi-infinite line with a reflecting boundary at the origin: Q(x,t) \sim t^{-N(N-1)/2}.Comment: 5 page

Correct extrapolation of overlap distribution in spin glasses

We study in d=3 dimensions the short range Ising spin glass with Jij=+/-1 couplings at T=0. We show that the overlap distribution is non-trivial in the limit of large system size.Comment: 6 pages, 3 figure

Numerical Evidence for Spontaneously Broken Replica Symmetry in 3D Spin Glasses

By numerical simulations of the $3d$ Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system.Comment: PHYSREV format, 2 .ps figures added with figure command in uufiles forma

New bounds for the free energy of directed polymers in dimension 1+1 and 1+2

We study the free energy of the directed polymer in random environment in dimension 1+1 and 1+2. For dimension 1, we improve the statement of Comets and Vargas concerning very strong disorder by giving sharp estimates on the free energy at high temperature. In dimension 2, we prove that very strong disorder holds at all temperatures, thus solving a long standing conjecture in the field.Comment: 31 pages, 4 figures, final version, accepted for publication in Communications in Mathematical Physic

Collinear N\'eel-type ordering in partially frustrated lattices

We consider two partially frustrated S = 1/2 antiferromagnetic spin systems on the triangular and pentagonal lattices. In an elementary plaquette of the two lattices, one bond has exchange interaction strength $\alpha$ ($\alpha \leq 1$) whereas all other bonds have exchange interaction strength unity. We show that for $\alpha$ less than a critical value $\alpha_{c}$, collinear N\'eel-type ordering is possible in the ground state. The ground state energy and the excitation spectrum have been determined using linear spin wave theory based on the Holstein-Primakoff transformation.Comment: Four pages, LaTeX, Four postscripts figures, Phys. Rev. B58, 73 (1998

Stretched Polymers in Random Environment

We survey recent results and open questions on the ballistic phase of stretched polymers in both annealed and quenched random environments.Comment: Dedicated to Erwin Bolthausen on the occasion of his 65th birthda

Interfaces (and Regional Congruence?) in Spin Glasses

We present a general theorem restricting properties of interfaces between thermodynamic states and apply it to the spin glass excitations observed numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3 and 4. We show that such excitations, with interface dimension smaller than d, cannot yield regionally congruent thermodynamic states. More generally, zero density interfaces of translation-covariant excitations cannot be pinned (by the disorder) in any d but rather must deflect to infinity in the thermodynamic limit. Additional consequences concerning regional congruence in spin glasses and other systems are discussed.Comment: 4 pages (ReVTeX); 1 figure; submitted to Physical Review Letter