order propagation in dilute antiferromagnetic potts models the possible orderings in a dilute antiferromagnetic q 3 potts model on a triangular lattice are studied by applying to a hierarchical lattice an approximate renormalisation group scheme which incorporates and preserves all the symmetries of the potts model this scheme indicates that states with partial order in which only a subset of the symmetries are broken can exist in systems with these symmetries they do not however occur in the model with nearest neighbour pair interactions only in this model the authors find solely the antiferromagnetically ordered states which occur for bond probabilities in excess of p1 which is greater than pc the critical probability for bond percolation

spanning forests and the q state potts model in the limit q 0 we study the q state potts model with nearest neighbor coupling v e j 1 in the limit q v 0 with the ratio w v q held fixed combinatorially this limit gives rise to the generating polynomial of spanning forests physically it provides information about the potts model phase diagram in the neighborhood of q v 0 0 we have studied this model on the square and triangular lattices using a transfer matrix approach at both real and complex values of w for both lattices we have computed the symbolic transfer matrices for cylindrical strips of widths 2 l 10 as well as the limiting curves b of partition function zeros in the complex w plane for real w we find two distinct phases separated by a transition point w w0 where w0 1 4 resp w0 0 1753 0 0002 for the square resp triangular lattice for w w0 we find a non critical disordered phase that is compatible with the predicted asymptotic freedom as w for w w0 our results are compatible with a massless berker kadanoff phase with central charge c 2 and leading thermal scaling dimension xt 1 2 marginally irrelevant operator at w w0 we find a first order critical point the first derivative of the free energy is discontinuous at w0 while the correlation length diverges as w w0 and is infinite at w w0 the critical ehavior at w w0 seems to be the same for both lattices and it differs from that of the berker kadanoff phase our results suggest that the central charge is c 1 the leading thermal scaling dimension is xt 1 0 and the critical exponents are 1 d 1 2 and 1

hausdorff operators on the power weighted hardy spaces abstract in this paper we study the high dimensional hausdorff operators on the power weighted hardy spaces we establish their sharp boundedness on power weighted hardy spaces and local hardy spaces particularly our results solve an open question posted by liflyand in 16

randomness induced evolution of first order to second order phase transition in the three state potts antiferromagnetic model on a triangular lattice the three state potts antiferromagnetic model on the two dimensional triangular lattice has a weak first order transition in the pure case our monte carlo simulation displays a transition temperature at t 0 628 which is consistent with previous studies the nature of phase transition due to the randomness of quenched bonds is considered in this study the energy histogram shows a single gaussian peak due to randomness of the bond while the first order phase transition displays distinct double peaks due to the coexistence of two states the histogram analysis ascertains the significance of order variation from the first order to the second order phase transition in this system

series analysis of tricritical behaviour mean field model and slicewise pade approximants a mean field model is proposed as a test case for tricritical series analysis methods derivation of the 50th order series for the magnetization is reported as the first application this series is analysed by the traditional slicewise pade approximant method popular in earlier studies of tricriticality

theory of morphological evolution in ostwald ripening abstract the multiple expansion theory for ostwald ripening in a three dimensional system is presented analogously to the case in two dimensional coarsening t imaeda and k kawasaki physica a 164 1990 335 the migration and the shape deformation of droplets caused by the diffusional interaction are taken into account in our kinetic equations of motion the derived equations can be solved numerically within a fairly resonable computation time the role of the mullins sekerka instability in the coarsening kinetics is examined

a rigorous theory of finite size scaling at first order phase transitions a large class of classical lattice models describing the coexistence of a finite number of stable states at low temperatures is considered the dependence of the finite volume magnetizationm per h l in cubes of sizel d under periodic boundary conditions on the external fieldh is analyzed for the case where two phases coexist at the infinite volume transition pointh t we prove that independent of the details of the model the finite volume magnetization per lattice site behaves likem per h t m tanh ml d h ht withm per h denoting the infinite volume magnetization and m 1 2 m per h t 0 m per h t 0 introducing the finite size transition pointh m l as the point where the finite volume susceptibility attains the maximum we show that in the case of asymmetric field driven transitions its shift ish t h m l o l 2d in contrast to claims in the literature starting from the obvious observation that the number of stable phases has a local maximum at the transition point we propose a new way of determining the pointh t from finite size data with a shift that is exponentially small inl finally the finite size effects are discussed also in the case where more than two phases coexist

three state potts antiferromagnet on the triangular lattice the three state potts antiferromagnetic model on the triangular lattice 3paft has a weak first order transition in the pure case the first order nature follows from analytic arguments and while it has been observed in some simulations the precision of and internal disagreement between these observations has left much to be desired the 3paft is the only two dimensional nearest neighbour potts model with an ordered phase that does not have an infinite degeneracy that remains without an exact value for its critical point this model is expected to exhibit interesting glassy behaviour and a possible crossover to a second order transition upon dilution a careful characterization of the nature of the pure transition is needed in order to explore the physics of the dilute model we find clear indication of a first order transition at tt 0 62731 or 0 00006 using a cluster method that can be extended to the dilute case and histogram reweighting analysis our estimate is two orders of magnitude more precise than previous simulations and falls within the error bounds of a reanalysis of existing series expansion tt 0 628 or 0 004 reported on herein

transfer matrices and partition function zeros for antiferromagnetic potts models iii triangular lattice chromatic polynomial we study the chromatic polynomial pg q for m n triangular lattice strips of widths m 12p 9f with periodic or free transverse boundary conditions respectively and arbitrary lengths n with free longitudinal boundary conditions the chromatic polynomial gives the zero temperature limit of the partition function for the q state potts antiferromagnet we compute the transfer matrix for such strips in the fortuin kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q plane in the limit n we recompute the limiting curve obtained by baxter in the thermodynamic limit m n and find new interesting features with possible physical consequences finally we analyze the isolated limiting points and their relation with the beraha numbers

a mapping relating complex and physical temperatures in the 2d q state potts model and some applications we show an exact equivalence of the free energy of the q state potts antiferromagnet on a lattice for the full temperature interval and the free energy of the q state potts model on the dual lattice for a semi infinite interval of complex temperatures cts this implies the existence of two quite different types of ct singularities the generic kind which does not obey universality or various scaling relations and a special kind which does obey such properties and encodes information of direct physical relevance we apply this observation to characterize ct properties of the potts model on several lattices to rule out two existing conjectures and to determine the critical value of q above which the potts antiferromagnet on the diced lattice has no phase transition

boundedness of multidimensional hausdorff operators on h1 rn abstract in this paper we consider the h 1 boundedness of multidimensional hausdorff operators defined by h a f x r n u f a u x d u where l l o c 1 r n a u a i j u i j 1 n is an n n matrix and each a i j u is a measurable function of u let b i j 1 n b i j for the matrix b b i j u i j 1 n we prove that h a is bounded from the hardy space h 1 to itself if r n u det a 1 u ln 1 a 1 u n det a 1 u d u our result improves known results in addition we show that the above condition is optimal in the size condition

triangular lattice potts models in this paper we study the 3 state potts model on the triangular lattice which has two and three site interactions using a peierls argument we obtain a rigorous bound on the transition temperature thereby disproving a conjecture on the location of its critical point low temperature series are generated and analyzed for three particular choices of the coupling constants a phase diagram is then drawn on the basis of these considerations our analysis indicates that the antiferromagnetic transition and the transition along the coexistence line are of first order implying the existence of a multicritical point in the ferromagnetic region relation of the triangularq state potts model with other lattice statistical problems is also discussed in particular an ashkin teller model and the hard hexagon lattice gas solved by baxter emerge as special cases in appropriate limits

boundedness of hausdorff operators on real hardy spaces h1 over locally compact groups abstract results of liflyand and collaborators on the boundedness of hausdorff operators on the hardy space h 1 over finite dimensional real space are generalized to the case of locally compact groups that are spaces of homogeneous type special cases and examples of compact lie groups homogeneous groups in particular the heisenberg group and finite dimensional spaces over division rings are considered in conclusion we solve for the space l 2 an open question on compactness of a hausdorff operator posed by liflyand

transfer matrices and partition function zeros for antiferromagnetic potts models i general theory and square lattice chromatic polynomial we study the chromatic polynomials zero temperature antiferromagnetic potts model partition functions p g q for m n rectangular subsets of the square lattice with m 8 free or periodic transverse boundary conditions and n arbitrary free longitudinal boundary conditions using a transfer matrix in the fortuin kasteleyn representation in particular we extract the limiting curves of partition function zeros when n which arise from the crossing in modulus of dominant eigenvalues beraha kahane weiss theorem we also provide evidence that the beraha numbers b2 b3 b4 b5 are limiting points of partition function zeros as n whenever the strip width m is 7 periodic transverse b c or 8 free transverse b c along the way we prove that a noninteger beraha number except perhaps b10 cannot be a chromatic root of any graph

the q state potts ferromagnet on d dimensional hypercubic lattices we use a high temperature star graph expansion to compute the free energy and the susceptibility of a q state potts model for arbitrary q on d dimensional hypercubic lattices the series are to order o 10 in the expansion variable nu ek 1 ek q 1 we show how to compute the expectation value of any operator on a finite graph for arbitrary number q of states of the potts model

hardy space estimates of hausdorff operators on the heisenberg group abstract this is a continuation of a series of works about hausdorff operator on hardy spaces in the setting of the heisenberg group in this paper we obtain the boundedness from lebesgue spaces to hardy spaces for fractional hausdorff operators and their compositions with riesz transforms we also establish the boundedness for two kinds of special hausdorff operators the hausdorff poisson operator and the hausdorff gauss operator on hardy spaces

high temperature series analyses of the classical heisenberg and xy models abstract although there is now a good measure of agreement between monte carlo and high temperature series expansion estimates for ising n 1 models published results for the critical temperature from series expansions up to 12th order for the three dimensional classical heisenberg n 3 and xy n 2 models do not agree very well with recent high precision monte carlo estimates in order to clarify this discrepancy we have analyzed extended high temperature series expansions of the susceptibility the second correlation moment and the second field derivative of the susceptibility which have been derived a few years ago by luscher and weisz for general o n vector spin models on d dimensional hypercubic lattices up to 14th order in k j kbt by analyzing these series expansions in three dimensions with two different methods that allow for confluent correction terms we obtain good agreement with the standard field theory exponent estimates and with the critical temperatures estimates from the new high precision monte carlo simulations furthermore for the heisenberg model we also reanalyze existing series for the susceptibility on the bcc lattice up to 11th order and on the fcc lattice up to 12th order using the same methods

multivariate hausdorff operators on the spaces lp rn abstract the operators h indicated in the title are characterized by a finite borel measure on r n a borel measurable function c on r n and an n n a e nonsingular matrix a whose entries are also borel measurable functions on r n and h f is defined by means of a lebesgue stieltjes integral with respect to we give simple sufficient conditions in order that these operators be bounded on the lebesgue spaces l p r n for some 1 p these sufficient conditions are exact even in the well known special cases of the cesaro and copson operators we also determine the hausdorff operator h which is adjoint to h in a certain sense we reveal interrelations among these operators and the fourier transform of a function f in l 1 r n on closing we present further special hausdorff operators