composition algebras with large derivation algebras abstract the finite dimensional flexible composition algebras include the hurwitz algebras composition algebras with unit element but also other interesting classes of algebras the para hurwitz and the okubo algebras the above mentioned algebras present many symmetries and this is reflected in their large derivation algebras in the present paper we study the opposite question what can be said about the composition algebras if we have some information about their derivation algebras our main result is the classification of all the composition algebras with such large derivation algebras

low temperature behavior of the multicomponent widom rowlison model on finite square lattices we consider the multicomponent widom rowlison with metropolis dynamics which describes the evolution of a particle system where m different types of particles interact subject to certain hard core constraints focusing on the scenario where the spatial structure is modeled by finite square lattices we study the asymptotic behavior of this interacting particle system in the low temperature regime analyzing the tunneling times between its m maximum occupancy configurations and the mixing time of the corresponding markov chain in particular we develop a novel combinatorial method that exploiting geometrical properties of the widom rowlinson configurations on finite square lattices leads to the identification of the timescale at which transitions between maximum occupancy configurations occur and shows how this depends on the chosen boundary conditions and the square lattice dimensions

on the gibbs states of the noncritical potts model on z 2 we prove that all gibbs states of the q state nearest neighbor potts model on mathbb z 2 below the critical temperature are convex combinations of the q pure phases in particular they are all translation invariant to achieve this goal we consider such models in large finite boxes with arbitrary boundary condition and prove that the center of the box lies deeply inside a pure phase with high probability our estimate of the finite volume error term is of essentially optimal order which stems from the brownian scaling of fluctuating interfaces the results hold at any supercritical value of the inverse temperature beta beta c q log left 1 sqrt q right

uniqueness and global markov property for euclidean fields the case of general polynomial interactions we give a general method for proving uniqueness and global markov property for euclidean quantum fields the method is based on uniform continuity of local specifications proved by using potential theoretical tools and exploitation of a suitable fkg order structure we apply this method to give a proof of uniqueness and global markov property for the gibbs states and to study extremality of gibbs states also in the case of non uniqueness in particular we prove extremality for 2 4 also in the case of non uniqueness and global markov property for weak coupling 2 4 which solves a long standing problem uniqueness and extremality holds also at any point of differentiability of the pressure with respect to the external magnetic field

phase transitions in the multicomponent widom rowlinson model and in hard cubes on the bcc lattice we use monte carlo techniques and analytical methods to study the phase diagram of the m component widom rowlinson model on the bcc lattice there are m species all with same fugacity z and a nearest neighbor hard core exclusion between unlike particles simulations show that for m 3 there is a crystal phase for z lying between zc m and zd m while for z zd m there are m demixed phases each consisting mostly of one species for m 2 there is a direct second order transition from the gas phase to the demixed phase while for m 3 the transition at zd m appears to be first order putting it in the potts model universality class for m large pirogov sinai theory gives zd m m 2 2 3m2 in the crystal phase the particles preferentially occupy one of the sublattices independent of species i e spatial symmetry but not particle symmetry is broken for m this transition approaches that of the one component hard cube gas with fugacity y zm we find by direct simulations of such a system a transition at yc 0 71 which is consistent with the simulation zc m for large m this transition appears to be always of the ising type

agreement percolation and phase coexistence in some gibbs systems we extend some relations between percolation and the dependence of gibbs states on boundary conditions known for ising ferromagnets to other systems and investigate their general validity percolation is defined in terms of the agreement of a configuration with one of the ground states of the system this extension is studied via examples and counterexamples including the antiferromagnetic ising and hard core models on bipartite lattices potts models and many layered ising and continuum widom rowlinson models in particular our results on the hard square lattice model make rigorous observations made by hu and mak on the basis of computer simulations moreover we observe that the naturally defined clusters of the widom rowlinson model play for the wr model itself the same role that the clusters of the fortuin kasteleyn measure play for the ferromagnetic potts models the phase transition and percolation in this system can be mapped into the corresponding liquid vapor transition of a one component fluid

a classical wr model with q particle types a version of the widom rowlinson model is considered where particles of q types coexist subject to pairwise hard core exclusions for q le 4 in the case of large equal fugacities we give a complete description of the pure phase picture based on the theory of dominant ground states

first order phase transitions in unbounded spin systems i construction of the phase diagram the phase diagram and the corresponding infinite volume gibbs states are constructed for a large class of continuous unbounded spin models our construction relies on a partition of unity mapping our system onto an interacting contour system a generalisation of zahradnik s approach to piragov sinai theory to interacting contour systems and a suitable mean field expansion around the minimas of the hamiltonian

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

quantum lattice models at intermediate temperature we analyze the free energy and construct the gibbs kms states for a class of quantum lattice systems at low temperature and when the interactions are almost diagonal in a suitable basis the models we study may have continuous symmetries our results however apply to intermediate temperatures where discrete symmetries are broken but continuous symmetries are not our results are based on quantum pirogov sinai theory and a combination of high and low temperature expansions

forbidden gap argument for phase transitions proved by means of chessboard estimates chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest in this note we show that the method not only produces a point in the phase diagram where more than one gibbs states coexist but that it can also be used to rule out the existence of shift ergodic states that differ significantly from those proved to exist for models depending on a parameter say the temperature this shows that the values of the conjugate thermodynamic quantity the energy inside the transitional gap are forbidden in all shift ergodic gibbs states we point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria

the q state potts model in the standard pirogov sinai theory surface tensions and wilson loops theq state potts model both scalar and gauge versions is rewritten with the help of the duality transformation into a form of the pirogov sinai theory with noninteracting contours that can be controlled by cluster expansions onceq is large enough this is then used in a new proof of the existence of a unique transition inverse temperature t where the mean internal energy is discontinuous moreover we prove for the scalar model again forq large enough that there are discontinuities at t of the magnetization and of the mass gap with the magnetization vanishing below t and the mass gap vanishing above t we also show that the surface tensions between ordered stable phases are strictly positive up to t and the surface tension between an ordered phase and the disordered one is strictly positive at t for the three dimensional gauge model the wilson parameter exhibits a direct transition from an area law decay quark confinement to a perimeter law decay deconfinement

on the singularity of the free energy at a first order phase transition at first order phase transition the free energy does not have an analytic continuation in the thermodynamical variable which is conjugate to an order parameter for the transition this result is proved at low temperature for lattice models with finite range interaction and two periodic ground states under the only condition that they satisfy the peierls condition

composition algebras satisfying certain identities abstract even though the class of power associative algebras is huge only hurwitz algebras appear in the case of composition algebras not necessarily unital over fields of characteristic different from two under this assumption and other conditions weaker than power associativity we study in this note composition algebras of arbitrary dimension first a characterization of hurwitz algebras is given when the ground field has at least five elements more cases are considered so by using conditions on powers of every element we characterize when a composition algebra over a field of characteristic different from 2 and 3 and with at least 7 elements is hurwitz or its norm is associative similar characterizations are given for composition algebras that are hurwitz or standard ii respectively hurwitz or standard iii

nonmonotonic behavior in hard core and widom rowlinson models we give two examples of nonmonotonic behavior in symmetric systems exhibiting more than one critical point at which spontaneous symmetry breaking appears or disappears the two systems are the hard core model and the widom rowlinson model and both examples take place on a variation of the cayley tree bethe lattice devised by schonmann and tanaka we obtain similar though less constructive examples of non monotonicity via certain local modifications of any graph e g the square lattice which is known to have a critical point for either model en route we prove that the widom rowlinson model does behave monotonically on the ordinary cayley tree and we obtain an explicit description of its critical behavior there we conclude with some results about monotonicity of the phase transition phenomenon relative to graph structure

an alternate version of pirogov sinai theory a new approach to the pirogov sinai theory of phase transitions is developed not employing the contour models with a parameter the completeness of the phase diagram is proven

a nonlinear empirical prescription for simultaneously interpolating and smoothing contours over an irregular grid a simple empirical interpolation procedure is developed based on the approximation that the magnitudes in the contouring space vary according to the inverse square of the distance this prescription is no more complicated than using linear interpolation but has the advantage that an interpolated point is now a function of its n nearest neighbours in all directions using such an interpolation approximation a method has been devised for tracing the contours through the reference grid points plus extra grid points whereby each triangular element now has 3d 3 extra grid points where d is the number of calculated points on each side of the triangle this procedure does not increase the computational burden but merely serves the purpose of guiding the path of the contour by taking into account the nonlinearity of the space between the original reference grid points within an inverse square approximation this technique has the added benefit that the resulting contours are simultaneously smoothed out

ordering and demixing transitions in multicomponent widom rowlinson models we use monte carlo techniques and analytical methods to study the phase diagram of multicomponent widom rowlinson models on a square lattice there are m species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles simulations show that for m between two and six there is a direct transition from the gas phase at z mathit z mathit d m to a demixed phase consisting mostly of one species at zg mathit z mathit d m while for m ensuremath ge 7 there is an intermediate crystal phase for z lying between mathit z mathit c m and mathit z mathit d m in this phase which is driven by entropy particles independent of species preferentially occupy one of the sublattices i e spatial symmetry but not particle symmetry is broken the transition at mathit z mathit d m appears to be of the first order for m ensuremath ge 5 putting it in the potts model universality class for large m the transition between the crystalline and demixed phases at mathit z mathit d m can be proven to be of the first order with mathit z mathit d m ensuremath sim m 2 1 m while mathit z mathit c m is argued to behave as ensuremath lambda mathrm cr m with ensuremath lambda mathrm cr the critical value of the fugacity at which the one component hard core square lattice gas has a transition and to be always of the ising type explicit calculations for the bethe lattice with the coordination number q 4 give results similar to those for the square lattice except that the transition at mathit z mathit d m becomes first order at mg2 this happens for all q consistent with the model being in the potts universality class c 1995 the american physical society

symmetric composition algebras abstract a construction of all the okubo algebras over fields of characteristic 3 is provided and the complete classification of the composition algebras with associative norm over fields is finished

paper identification and optimal estimation of random fields from scattered point wise data a self contained presentation of the interpolation problem in two dimensional spatial random fields is given we investigate the case where the random field is not necessarily stationary where the data are so scarce and so scattered in space that sample covariance function estimates are not meaningful and where therefore an analytical parametric variogram model is used in lieu of the covariance we discuss several variogram parameter estimation techniques ls gls ml interpolation error method and we show how to derive estimates of various functionals of the random field from the variogram a numerical simulation and two typical engineering applications illustrate the variogram estimation techniques and provide a good measure of their respective performances

analyticity of low temperature phase diagrams of lattice spin models the analyticity of all strata of the pirogov sinai phase diagram is proved as a byproduct of the method a characterization of typical volumes for which the complex partition function vanishes is given for a hamiltonian that is a perturbation of the real valued one near the point of a phase transition

finite size scaling for first order phase transitions rigorous results abstract recent rigorous results on finite size effects for lattice models are reviewed we consider symmetric and asymmetric first order phase transitions in cubic and cylindrical geometries and discuss the determination of transition points from finite size data

comment on a nonlinear empirical prescription for simultaneously interpolating and smoothing contours over an irregular grid by f duggan abstract the article discussed introduces inverse distance weighting idw as an interpolation technique for scattered measurements idw has been extensively researched and tested and its limitations widely published in the present context however it is considered desirable to augment duggan s contribution by enumerating the drawbacks of the method other aspects of the article which require particular clarification are also noted

an integral equation theory for the widom rowlinson mixture the widom rowlinson mixture is a two component fluid in which like species do not interact and unlike species interact via a hard core repulsion as the density is increased this fluid phase separates standard integral equation approaches such as the percus yevick or hypernetted chain or thermodynamically self consistent hybirds of these two make very inaccurate predictions for the location of this critical point in the three dimensional model in this article we suggest a family of new approximations for this model that rely on incorporating terms in the density expansion of the direct correlation function into the closure approximation we show that the simplest of these closures is significantly more accurate than previous theories for the structure and thermodynamics of the fluid

on the ising model with random boundary condition the infinite volume limit behavior of the 2d ising model under possibly strong random boundary conditions is studied the model exhibits chaotic size dependence at low temperatures and we prove that the and phases are the only almost sure limit gibbs measures assuming that the limit is taken along a sparse enough sequence of squares in particular we provide an argument to show that in a sufficiently large volume a typical spin configuration under a typical boundary condition contains no interfaces in order to exclude mixtures as possible limit points a detailed multi scale contour analysis is performed

automatic interpolation methods for mapping piezometric surfaces abstract the purpose of analysis of spatial data should determine the approach to be adopted if estimation is concerned with detailed local interpretation rather than some form of global averaging then kriging would seem to be an inappropriate method this is especially so for the interpolation of precise observations which consequently are better estimated by deterministic methods five such efficient direct automatic interpolation methods are discussed and applied to the contour mapping of a piezometric surface