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We consider Schloegl models (or contact processes) where particles on a square grid annihilate at a rate p and are created at a rate of kn=n(n-1)/[N(N-1)] at empty sites with n particles in a neighborhood ΩN of size N. Simulation reveals a discontinuous transition between populated and vacuum states, but equistable p=peq determined by the stationarity of planar interfaces between these states depends on the interface orientation and on ΩN. The behavior for large ΩN follows from continuum equations. These also depend on the interface orientation and on ΩN shape, but a unique peq=0.211 376 320 4 emerges imposing a Gibbs phase rule. [ABSTRACT FROM AUTHOR]

By adsorbing the same species onto both sides of a suspended, atomically thin membrane, it is possible to couple two distinct surface adsorption systems. This new system, with reflection symmetry about the membrane, is described by a phase diagram with two axes, both representing the chemical potential of the same element, but in distinct half-spaces. For the case of potassium adsorption onto a graphene membrane, the result is a devil's staircase of fractions for the proportion of adsorbates adhered to one side. Fractions with simpler denominators are favored across wider regions of chemical potential, a pattern reminiscent of other fractional systems across a wide range of physics. Since the system can support multiple devil's staircases each at a distinct overall adsorbate areal density, points along the boundary between adjacent staircases can come arbitrarily close to violating the Gibbs phase rule. This dual-sided adsorbate geometry provides a means to explore surface science for pairs of weakly coupled surfaces. [ABSTRACT FROM AUTHOR]

We propose a quantum algorithm for many-body state preparation. It is especially suited for injective projected entangled pair states and thermal states of local commuting Hamiltonians on a lattice. We show that for a uniform gap and sufficiently smooth paths, an adiabatic runtime and circuit depth of O(polylogN) can be achieved for O(N) spins. This is an almost exponential improvement over previous bounds. The total number of elementary gates scales as O(NpolylogN). This is also faster than the best known upper bound of O(N²) on the mixing times of Monte Carlo Markov chain algorithms for sampling classical systems in thermal equilibrium. [ABSTRACT FROM AUTHOR]