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The raise and peel model is a one-dimensional stochastic model of a fluctuating interface with nonlocal interactions. This is an interesting physical model, in this paper we review its properties. Itâ€™s phase diagram has a massive phase and a gapless phase with varying critical exponents. At the phase transition point, the model exhibits conformal invarianceâ€¦ (More)

- F. C. Alcaraz, Vladimir Rittenberg, M. Scheunert
- 1994

We consider an extension of the (tâ€“U) Hubbard model taking into account new interactions between the numbers of up and down electrons. We confine ourselves to a one-dimensional open chain with L sites (4L states) and derive the effective Hamiltonian in the strong repulsion (large U) regime. This Hamiltonian acts on 3L states. We show that the spectrum ofâ€¦ (More)

The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a SchrÃ¶dinger equation in which the wave function is the probability distribution and the Hamiltonian is that of a quantum chain with nearest neighbor interactions. Since manyâ€¦ (More)

- F. C. Alcaraz
- 1993

We show that the master equation governing the dynamics of simple diffusion and certain chemical reaction processes in one dimension give time evolution operators (Hamiltonians) which are realizations of Hecke algebras. In the case of simple diffusion one obtains, after similarity transformations, reducible hermitian representations while in the other casesâ€¦ (More)

- F. C. Alcaraz
- 1998

Stationary probability distributions for stochastic processes on linear chains with closed or open ends are obtained using the matrix product Ansatz. The matrices are representations of some quadratic algebras. The algebras and the types of representations considered depend on the boundary conditions. In the language of quantum chains we obtain the groundâ€¦ (More)

- F. C. Alcaraz, Erel Levine
- 2006

Using Monte-Carlo simulations on large lattices, we study the effects of changing the parameter u (the ratio of the adsorption and desorption rates) of the raise and peel model. This is a nonlocal stochastic model of a fluctuating interface. We show that for 0 < u < 1 the system is massive, for u = 1 it is massless and conformal invariant. For u > 1 theâ€¦ (More)

- F. C. Alcaraz, Miguel IbÃ¡Ã±ez Berganza, German Sierra
- Physical review letters
- 2011

In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and RÃ©nyi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalizeâ€¦ (More)

Most of the exact solutions of quantum one-dimensional Hamiltonians are obtained thanks to the success of the Bethe ansatz on its several formulations. According to this ansatz the amplitudes of the eigenfunctions of the Hamiltonian are given by a sum of permutations of appropriate plane waves. In this paper, alternatively, we present a matrix productâ€¦ (More)

- F. C. Alcaraz, R. Z. Bariev
- Physical review. E, Statistical physics, plasmasâ€¦
- 1999

A generalization of the simple exclusion asymmetric model is introduced. In this model an arbitrary mixture of molecules with distinct sizes s=0,1,2, ..., in units of lattice space, diffuses asymmetrically on the lattice. A related surface growth model is also presented. Variations of the distribution of the molecules sizes may change the excluded volumeâ€¦ (More)

We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in a disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied using Monte Carlo simulations. We point out aâ€¦ (More)