conformal invariance and critical dynamics the author discusses the behaviour of dynamic correlation functions under conformal transformations in particular the exact form of the dynamic scaling function at the critical point for an arbitrary isotropic two dimensional model is obtained with either conserved or nonconserved order parameter

equivariant cohomology fock space and loop groups equivariant de rham cohomology is extended to the infinite dimensional setting of a loop subgroup acting on a loop group using hida supersymmetric fock space for the weil algebra and malliavin test forms on the loop group the mathai quillen isomorphism in the brst formalism of kalkman is defined so that the equivalence of various models of the equivariant de rham cohomology can be established

trees and branches in banach spaces an infinite dimensional notion of asymptotic structure is considered this notion is developed in terms of trees and branches on banach spaces every countably infinite countably branching tree t of a certain type on a space x is presumed to have a branch with some property it is shown that then x can be embedded into a space with an fdd e i so that all normalized sequences in x which are almost a skipped blocking of e i have that property as an application of our work we prove that if x is a separable reflexive banach space and for some 1 0 there exists a subspace of x having finite codimension which c 2 e embeds into the l p sum of finite dimensional spaces

monte carlo computation of cluster free energies in the ising model a test for the validity of the capillarity approximation a new monte carlo technique is proposed to compute directly the free energy difference fn 1 fn of two clusters with size n 1 and n the algorithm is applied to the two dimensional square ising model with nearest neighbour interactions results are given for 1 9 but for smaller cluster sizes the obtained energies are larger than predicted by the capillarity model the deviation exhibits no systematic size dependence but a strong temperature dependence the existence of a size independent term in fn is confirmed by the values of the internal energy un obtained as a by product of the calculation

schreier sets in ramsey theory we show that ramsey theory a domain presently conceived to guaran tee the existence of large homogeneous sets for partitions on k tuples of words for every natural number k over a finite alphabet can be extended to one for partitions on schreier type sets of words of every countable ordinal indeed we establish an extension of the partition theorem of carlson about words and of the more general partition theorem of furstenberg katznelson about combinatorial subspaces of the set of words generating from k tuples of words for any fixed natural number k into a partition theorem about combinatorial subspaces generating from schreier type sets of words of order any fixed countable ordinal furthermore as a result we obtain a strengthening of carlson s infinitary nash williams type and ellentuck type partition theorem about infinite sequences of variable words into a theorem in which an infinite sequence of variable words and a binary partition of all the finite sequences of words one of whose components is in addition a tree are assumed concluding that all the schreier type finite reductions of an infinite reduction of the given sequence have a be havior determined by the cantor bendixson ordinal index of the tree component of the partition falling in the tree component above that index and in its complement below it

on the complexity of some inevitable classes of separable banach spaces abstract in this paper we study the descriptive complexity of some inevitable classes of banach spaces precisely as shown in 11 every banach space either contains a hereditarily indecomposable subspace or an unconditional basis and as shown in 8 every banach space either contains a minimal subspace or a continuously tight subspace in this note we study the complexity of those inevitable classes as well as the complexity of containing a subspace in any of those classes

coding into ramsey sets in 6 w t gowers formulated and proved a ramsey type result which lies at the heart of his famous dichotomy for banach spaces he defines the notion of weakly ramsey set of block sequences of an infinite dimensional banach space and shows that every analytic set of block sequences is weakly ramsey we show here that gowers result follows quite directly from the fact that all g sets are weakly ramsey if the banach space does not contain c0 and from the fact that all f sets are weakly ramsey in the case of an arbitrary banach space we also show that every result obtained by the application of gowers theorem to an analytic set can also be obtained by applying the theorem to a f set or to a g set if the space does not contain c0 this fact explains why the only known applications of this technique are based on very low ranked borel sets open closed f or g

on the number of permutatively inequivalent basic sequences in a banach space let x be a banach space with a schauder basis en n n the relation e0 is borel reducible to permutative equivalence between normalized block sequences of en n n or x is c0 or lp saturated for some 1 p if en n n is shrinking unconditional then either it is equivalent to the canonical basis of c0 or lp 1 p or the relation e0 is borel reducible to permutative equivalence between sequences of normalized disjoint blocks of x or of x if en n n is unconditional then either x is isomorphic to l2 or x contains 2 subspaces or 2 quotients which are spanned by pairwise permutatively inequivalent normalized unconditional bases

an infinite ramsey theorem and some banach space dichotomies a problem of banach asks whether every infinite dimensional banach space which is isomorphic to all its infinite dimensional subspaces must be isomorphic to a separable hilbert space in this paper we prove a result of a ramsey theoretic nature which implies an interesting dichotomy for subspaces of banach spaces combined with a result of komorowski and tomczakjaegermann this gives a positive answer to banachxs problem we then generalize the ramsey theoretic result and deduce a further dichotomy for banach spaces with an unconditional basis

non perturbative renormalization using dimensional regularization applications to the epsilon expansion the authors give a prescription for the one loop renormalisation of the imaginary parts of vertex functions in g phi 4 which are generated when g 0 within the dimensional regularisation scheme this involves another non perturbative renormalisation over and above the usual one loop perturbative renormalisation the authors use an extended minimal subtraction scheme so that the resulting renormalisation group functions have a simple dependence on epsilon 4 d in contrast to the usual case however both the beta function and the renormalised coupling gr are in general complex for real g and the fixed point for epsilon gr 0 is non perturbative in epsilon this fixed point determines the imaginary parts of the critical exponents which are generated when epsilon 0 and allows the determination of the high order behaviour of the perturbation series in epsilon for these exponents the generalisation of these ideas to the o n symmetric g phi 2 2 model is also given

modified mixed tsirelson spaces we study the modified and boundedly modified mixed tsirelson spacestm fkn n n 1 andtm s fkn n n 1 respectively defined by a subsequence fkn of the sequence of schreier families fn these are reflexive asymptotic l1spaces with an unconditional basis ei ihaving the property that every sequence xi ni 1of normalized disjointly supported vectors contained in ei i nis equivalent to the basis of ln1 we show that if lim 1 nn 1 then the spacet fn n n 1 and its modified variationstm fn n n 1 ortm s fn n n 1 are totally incomparable by proving thatc0is finitely disjointly representable in every block subspace oft fn n n 1 next we present an example of a boundedly modified mixed tsirelson spacexm 1 u tm 1 fkn n n 1 which is arbitrarily distortable finally we construct a variation of the spacexm 1 uwhich is hereditarily indecomposable

banach spaces without minimal subspaces abstract we prove three new dichotomies for banach spaces a la w t gowers dichotomies the three dichotomies characterise respectively the spaces having no minimal subspaces having no subsequentially minimal basic sequences and having no subspaces crudely finitely representable in all of their subspaces we subsequently use these results to make progress on gowers program of classifying banach spaces by finding characteristic spaces present in every space also the results are used to embed any partial order of size 1 into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability

droplet structure in ising and potts models the structure of a recently introduced droplet in the q state potts model is analysed the authors derive exact relations from which it follows that the incipient infinite droplet at the critical temperature is a self similar fractal made of links and blobs just as recently found in random percolation the number of links nlinks between two points separated by a distance of the order b is given by nlinks varies as b1 nu b q where nu b q is the connectedness length exponent when t tc q and pb is used as an independent variable this result and the available calculations of nu b q indicate that the number of links decreases as q increases an analysis of the structure of the usual clusters made of nearest neighbour sites in a given potts site configuration is also made in particular it shows that for d 2 the incipient infinite cluster is made only of blobs and no links

on the hereditary proximity to l1 in the first part of the paper we present and discuss concepts of local and asymptotic hereditary proximity to l1 the second part is devoted to a complete separation of the hereditary local proximity to l1 from the asymptotic one more precisely for every countable ordinal we construct a separable reflexive space x such that every infinite dimensional subspace of it has bourgain l1 index greater than and the space itself has no l1 spreading model we also present a reflexive hi space admitting no lp as a spreading model

α minimal banach spaces a banach space w with a schauder basis is said to be minimal for some 1 if for any two block subspaces z y w the bourgain embeddability index of z into y is at least we prove a dichotomy that characterises when a banach space has an minimal subspace which contributes to the ongoing project initiated by w t gowers of classifying separable banach spaces by identifying characteristic subspaces

droplet theory of correlations in ordered phases the explicit droplet theory of low dimensional phase transitions developed recently is extended to yield a description of the pair correlation function for the universality class of q state potts models in the ordered phase and in zero external field it is shown that in d 1 epsilon dimensions the short distance behaviour of the correlation function and in particular the exponent eta are controlled by nested nearly spherical droplets in contrast it is argued that the spatial dependence of the large distance behaviour in d 2 or above is controlled by highly anisotropic droplets thus illuminating the widom relation sigma xi d 1 approximately constant linking the dimensionless surface tension sigma and the bulk correlation length xi in the particular case of d 2 the statistical weight of the relevant droplets is determined as that of two appropriately interacting strings in the spirit of recent independent arguments by abraham and by fisher a non ornstein zernike correlation function prefactor and the result of sigma xi 1 2 follow in accord with exact results for the q 2 ising case and with implications for the q to 1 percolation problem

the ising model below tc calculation of nonuniversal amplitudes using a primitive droplet model using recent exact results for the surface free energies of ising droplets on a square lattice and applying a primitive droplet theory due to langer 1967 the author obtains an expression for the principal nonuniversal amplitude appearing in the imaginary part of the analytic continuation of the free energy across the coexistence line for the square lattice ising model below tc the significance of this calculation is the known dependence on this amplitude of the large order terms in the expansion of the physical free energy in powers of h thus allowing a direct numerical comparison with existing series data to be made after carrying out a simple renormalisation of the droplet volume term the author finds excellent numerical agreement

time coarse graining near critical points the authors investigate the statistical properties of local variables coarse grained in time in systems undergoing continuous phase transitions a general theory is developed which suggests universal scaling behaviour in the limit of large coarse graining times the predictions are substantiated with monte carlo studies of two dimensional scalar models a simple fractal model of the time profile of the ordering variable is developed which captures and illuminates its timescale invariant character the theory is used to study the critical behaviour of local resonance lineshapes in the two dimensional case studied explicitly the critical slowing down is shown to drive a crossover to a split slow motion lineshape

ergodic banach spaces abstract we show that any banach space contains a continuum of non isomorphic subspaces or a minimal subspace we define an ergodic banach space x as a space such that e 0 borel reduces to isomorphism on the set of subspaces of x and show that every banach space is either ergodic or contains a subspace with an unconditional basis which is complementably universal for the family of its block subspaces we also use our methods to get uniformity results we show that an unconditional basis of a banach space of which every block subspace is complemented must be asymptotically c 0 or l p and we deduce some new characterisations of the classical spaces c 0 and l p

uniqueness of complex structure and real hereditarily indecomposable banach spaces there exists a real hereditarily indecomposable banach space x x c respectively x x h such that the algebra l x s x is isomorphic to c respectively to the quaternionic division algebra h up to isomorphism x c has exactly two complex structures which are conjugate totally incomparable and both hereditarily indecomposable so there exist two banach spaces which are isometric as real spaces but totally incomparable as complex spaces this extends results of j bourgain and s szarek j bourgain real isomorphic complex banach spaces need not be complex isomorphic proc amer math soc 96 2 1986 221 226 s szarek on the existence and uniqueness of complex structure and spaces with few operators trans amer math soc 293 1 1986 339 353 s szarek a superreflexive banach space which does not admit complex structure proc amer math soc 97 3 1986 437 444 and proves that a theorem of g godefroy and n j kalton g godefroy n j kalton lipschitz free banach spaces studia math 159 1 2003 121 141 about isometric embeddings of separable real banach spaces does not extend to the complex case the quaternionic example x h on the other hand has unique complex structure up to isomorphism other examples with a unique complex structure are produced including a space with an unconditional basis and non isomorphic to l2 this answers a question of s szarek in s szarek a superreflexive banach space which does not admit complex structure proc amer math soc 97 3 1986 437 444

universal local dynamics the authors suggest that near a critical point the statistical behaviour of local variables averaged over times long on microscopic scales is universal reflecting large scale partial structure the contention is supported with monte carlo studies of two dimensional scalar models

cluster size distribution above the percolation threshold discusses how the cluster size distribution above the percolation threshold is related to the existence of metastable states of the potts model the authors thus find that the average number of clusters per site containing n sites is given by c n approximately n theta exp constant n1 1 d where d is the dimensionality of the lattice the exponent theta is given for a range of values of d

a c_0 saturated banach space with no long unconditional basic sequences we present a banach space mathfrak x with a schauder basis of length omega 1 which is saturated by copies of c 0 and such that for every closed decomposition of a closed subspace x x 0 oplus x 1 either x 0 or x 1 has to be separable this can be considered as the non separable counterpart of the notion of hereditarily indecomposable space indeed the subspaces of mathfrak x have few operators in the sense that every bounded operator t x rightarrow mathfrak x from a subspace x of mathfrak x into mathfrak x is the sum of a multiple of the inclusion and a omega 1 singular operator i e an operator s which is not an isomorphism on any non separable subspace of x we also show that while mathfrak x is not distortable being c 0 saturated it is arbitrarily omega 1 distortable in the sense that for every lambda 1 there is an equivalent norm cdot on mathfrak x such that for every non separable subspace x of mathfrak x there are x y in s x such that cdot cdot ge la

numerical tests of nucleation theories for the ising models the classical nucleation theory cnt is tested systematically by computer simulations of the two dimensional 2d and three dimensional 3d ising models with a glauber type spin flip dynamics while previous studies suggested potential problems with cnt our numerical results show that the fundamental assumption of cnt is correct in particular the becker doring theory accurately predicts the nucleation rate if the correct droplet free energy function is provided as input this validates the coarse graining of the system into a one dimensional markov chain with the largest droplet size as the reaction coordinate furthermore in the 2d ising model the droplet free energy predicted by cnt matches numerical results very well after a logarithmic correction term from langer s field theory and a constant correction term are added but significant discrepancies are found between the numerical results and existing theories on the magnitude of the logarithmic correction term in the 3d ising model our analysis underscores the importance of correctly accounting for the temperature dependence of surface energy when comparing numerical results and nucleation theories

existence theorem for gauge algebra a general gauge action is defined by postulating a minimum of its properties necessary for the existence of loop expansion in the quantum theory the structure of the general gauge algebra is derived from these postulates the proof of existence of the structure functions lacking in previous works is given the question of uniqueness is also completely cleared up some unsolved problems are discussed in connection with the covariant quantization conjecture

finite size scaling study of the equilibrium cluster distribution of the two dimensional ising model the authors use a very fast and efficient algorithm to study by monte carlo methods the equilibrium cluster distribution cl l and the mean number of clusters per lattice site containing l particles in a square lattice of l2 sites of the two dimensional ising model at the critical point finite size scaling theory is then used to analyse the scaling ansatz cl l l tau f ls l tau and s being critical exponents the second moment of the cluster distribution p2 l sigma l2cl is shown to behave as p2 l approximately ltheta with theta 1 895 or 0 010 the effect of corrections to scaling is also discussed

a banach space block finitely universal for monotone bases a reflexive banach space x with a basis ei is constructed having the property that every monotone basis is block finitely representable in each block basis of x

scaling at the percolation threshold above six dimensions the fractal dimensionality of the infinite cluster at the percolation threshold for dimensionalities d 6 is shown to be d 4 rather than the naive finite size scaling prediction d d 2 similarly the conductivity of a sample of size l scales as l d rather than l 6 this anomalous behaviour is related to a dangerous irrelevant variable associated with the probability to have vertices of three bonds the crossover to the homogeneous behaviour occurs at length scales which are short compared with the correlation length the links and blobs picture is confirmed for d 6 and the size of the latter is estimated

geometric and algebraic reduction for singular momentum maps this paper concerns the reduction of singular constraint sets of symplectic manifolds it develops a geometric reduction procedure as well as continues the work of sniatycki and patrick on reduction a la dirac the relationships among the dirac geometric and sniatycki weinstein algebraic reduction procedures are studied primary emphasis is placed on the case where the constraints are given by the vanishing of a singular momentum map associated to the hamiltonian action of a compact lie group specifically an explicit local normal form is given for the momentum map which is used to show that these various reductions are all well defined and a necessary and sufficient condition for them to agree is derived related conditions are investigated and shown to be sufficient in the case of torus actions numerous examples are computed illustrating the results some discussion and examples are given for the noncompact case

a dual form of ramsey s theorem abstract let k where is the set of all natural numbers ramsey s theorem deals with colorings of the k element subsets of our dual form deals with colorings of the k element partitions of let k respectively be the set of all partitions of having exactly k respectively infinitely many blocks given x let x k be the set of all y k such that y is coarser than x dual ramsey theorem if k c 0 c t 1 where each c i is borel then there exists x such that x k c i for some i l dual galvin prikry theorem same as before with k replaced by we also obtain dual forms of theorems of ellentuck and mathias our results also provide an infinitary generalization of the graham rothschild parameter set theorem trans amer math soc 159 1971 257 292 and a new proof of the halpern lauchli theorem trans amer math soc 124 1966 360 367

an unconditionally saturated banach space with the scalar plus compact property abstract we construct a bourgain delbaen l space x k u s with structure that is strongly heterogeneous any bounded operator on x k u s is a compact perturbation of a multiple of the identity whereas the space x k u s is saturated with unconditional basic sequences

the unconditional basic sequence problem we construct a banach space that does not contain any infinite un conditional basic sequence and investigate further properties of this space for example it has no subspace that can be written as a topological direct sum of two infinite dimensional spaces this property implies that every operator on the space is a strictly singular perturbation of a multiple of the identity in par ticular it is either strictly singular or fredholm with index zero this implies that the space is not isomorphic to any proper subspace trinity college cambridge cb2 1tq england current address department of mathematics university college london gower street lon don wc1e 6bt england e mail address wtg l o phx cam ac uk universit paris vii u f r de mathtmatiques 2 place jussieu 75251 paris cedex 05 france current address equipe d analyse et mathematiques appliquees universite de mamne la vallee 93160 noisy le grand france e mail address maurey logiquejussieu fr this content downloaded from 157 55 39 105 on fri 07 oct 2016 04 30 48 utc all use subject to http about jstor org terms

existence uniqueness and cohomology of the classical brst charge with ghosts of ghosts a complete canonical formulation of the brst theory of systems with redundant gauge symmetries is presented these systems includep form gauge fields the superparticle and the superstring we first define the koszul tate differential and explicitly show how the introduction of the momenta conjugate to the ghosts of ghosts makes it acyclic the global existence of the brst generator is then demonstrated and the brst charge is proved to be unique up to canonical transformations in the extended phase space which includes the ghosts finally the brst cohomology in classical mechanics is investigated and shown to be equal to the cohomology of the exterior derivative along the gauge orbits as in the irreducible case this is done by re expressing the exterior algebra along the gauge orbits as a free differential algebra containing generators of higher degree which are identified with the ghosts of ghosts the quantum cohomology is not dealt with

a class of banach spaces with few non strictly singular operators we construct a family x of reflexive banach spaces with long countable as well as uncountable transfinite bases but with no unconditional basic sequences the method we introduce to achieve this allows us to considerably control the structure of subspaces of the resulting spaces as well as to precisely describe the corresponding spaces on non strictly singular operators for example for every pair of countable ordinals we are able to decompose every bounded linear operator from x to x as the sum of a diagonal operator and an strictly singular operator we also show that every finite dimensional subspace of any member x of our class can be moved by and 4 isomorphism to essentially any region of any other member x or our class finally we find subspaces x of x such that the operator space l x x is quite rich but any bounded operator t from x into x is a strictly singular pertubation of a scalar multiple of the identity

droplet theory in low dimensions ising systems in zero field the authors develop a theory of the universal configurational physics underlying critical point phenomena in the ising universality class the theory is formally justifiable in d 1 epsilon dimensions and may be regarded as the natural continuation of the kink based theory of one dimension which it incorporates as a limiting case in d 1 epsilon the configurational building block is the droplet the typical droplet is not spherical and the many droplet assembly is not dilute the implied problems are handled with renormalisation group methods it is found that droplet shape fluctuation effects control the correlation length exponent nu while the nesting of droplets within droplets control the order parameter exponent beta the exponents nu and beta thus effectively define respectively the fractal dimensions of the droplet surface and the droplet volume the theory is used to determine and illuminate the critical behaviour of further quantities including the free energy the susceptibility the droplet number distribution and the distribution of the intra droplet order

isomorphisms and strictly singular operators in mixed tsirelson spaces abstract we study the family of isomorphisms and strictly singular operators in mixed tsirelson spaces and their modified versions setting we show sequential minimality of modified mixed tsirelson spaces t m s n n n satisfying some regularity conditions and present results on existence of strictly singular non compact operators on subspaces of mixed tsirelson spaces defined by the families a n n and s n n

hamiltonian brst anti brst theory the hamiltonian brst anti brst theory is developed in the general case of arbitrary reducible first class systems this is done by extending the methods of homological perturbation theory originally based on the use of a single resolution to the case of a biresolution the brst and the anti brst generators are shown to exist the respective links with the ordinary brst formulation and with thesp 2 covariant formalism are also established

on uniformly finitely extensible banach spaces abstract we continue the study of uniformly finitely extensible banach spaces in short ufo initiated in moreno and plichko 2009 39 and castillo and plichko 2010 18 we show that they have the uniform approximation property of pelczynski and rosenthal and are compactly extensible we will also consider their connection with the automorphic space problem of lindenstrauss and rosenthal do there exist automorphic spaces other than c 0 i and l 2 i showing that a space all whose subspaces are ufo must be automorphic when it is hereditarily indecomposable hi and a hilbert space when it is either locally minimal or isomorphic to its square we will finally show that most hi among them the super reflexive hi space constructed by ferenczi and asymptotically l 2 spaces in the literature cannot be automorphic

bfv complex and higher homotopy structures we present a connection between the bfv complex abbreviation for batalin fradkin vilkovisky complex and the strong homotopy lie algebroid associated to a coisotropic submanifold of a poisson manifold we prove that the latter structure can be derived from the bfv complex by means of homotopy transfer along contractions consequently the bfv complex and the strong homotopy lie algebroid structure are l quasi isomorphic and control the same formal deformation problem

brst cohomology in classical mechanics the classical non quantum cohomology of the becchi rouet stora tyutin brst symmetry in phase space is defined and worked out no group action for the gauge transformations is assumed the results cover therefore the general case of an open algebra and are valid off shell each cohomology class contains all brst invariant functions with fixed ghost number an integer which differ from each other by a brst variation if the ghost number is negative there is only the trivial class whose elements are equivalent to zero if the ghost number is positive or zero there is a bijective correspondence between the brst classes and those of the exterior derivative along the gauge orbits these gauge orbits lie in the phase space surface on which the gauge generators are constrained to vanish the brst invariant functions of ghost numberp are then related to closedp forms along the orbits the addition of a brst variation corresponds to the addition of an exact form some comments about the quantum case are included the physical meaning of the classes with ghost number greater than zero is not discussed

determinacy and weakly ramsey sets in banach spaces we give a sufficient condition for a set of block subspaces in an infinite dimensional banach space to be weakly ramsey using this condition we prove that in the levy collapse of a mahlo cardinal every projective set is weakly ramsey this together with a construction of w h woodin is used to show that the axiom of projective determinacy implies that every projective set is weakly ramsey in the case of c 0 we prove similar results for a stronger ramsey property and for hereditarily indecomposable spaces we show that the axiom of determinacy plus the axiom of dependent choices imply that every set is weakly ramsey these results are the generalizations to the class of projective sets of some theorems from w t gowers and our paper weakly ramsey sets in banach spaces

the sh lie structure of poisson brackets in field theory a general construction of an sh lie algebra l algebra from a homological resolution of a lie algebra is given it is applied to the space of local functionals equipped with a poisson bracket induced by a bracket for local functions along the lines suggested by gel fand dickey and dorfman in this way higher order maps are constructed which combine to form an sh lie algebra on the graded differential algebra of horizontal forms the same construction applies for graded brackets in field theory such as the batalin fradkin vilkovisky bracket of the hamiltonian brst theory or the batalin vilkovisky antibracket

droplet theory in low dimensions potts models and percolation a recently developed droplet theory of low dimensional ising systems is generalised to describe the q state potts universality class and thence the percolation problem realised in the q to 1 limit an integral equation for the potts model free energy is derived and used to obtain the generating function for the cluster size probability distribution in the percolation problem above the percolation threshold a closed equation for the distribution is obtained and shown to yield scaling behaviour the form of the distribution is determined analytically in the regimes of small and large cluster sizes yielding respectively power law decay and kunz souillard exponential decay the form of the distribution in the regime of intermediate cluster sizes is determined numerically in space dimension d 2

subsequential minimality in gowers and maurey spaces we define block sequences xn in every block subspace of a variant of the space of gowers and maurey so that the map x2n 1 7 x2n extends to an isomorphism this implies the existence of a subsequentially minimal hi space which solves a question in fr1

stability of the isotropic fixed point near one dimension within the context of the l epsilon expansion and the near planar interface hamiltonian the isotropic fixed point is found to be stable to a wide class of perturbations in particular the universality class includes all non singular forms of anisotropic surface tension

weakly ramsey sets in banach spaces gowers analysis of the combinatorial content of his celebrated dichotomy for infinite dimensional separable banach spaces 7 led him to the formulation of the property of being weakly ramsey applied to sets of block bases a combinatorial notion related to the classical ramsey property for infinite sets of positive integers let n be the set of all infinite sets of positive integers with the natural topology induced by the cantor space via characteristic functions n is a polish space a subset n is ramsey if there exists a n such that either a or a where a is the set of all infinite subsets of a the famous galvin prikry theorem asserts that every borel subset of n is ramsey 4 or equivalently that every borel map from n into a finite space is constant on a cube a silver 17 shows that in fact all analytic subsets of n i e the continuous images of borel sets are ramsey a simpler more combinatorial proof is given by ellentuck 3 the ramsey property for more complex subsets of n turns out to depend essentially on the axioms of set theory thus for instance while go del s axiom of constructibility implies that some continuous image of a co analytic set is not ramsey see 9 martin s axiom implies that all such sets are ramsey 17 furthermore large cardinal axioms or determinacy axioms imply that all projective or doi 10 1006 aima 2001 1983 available online at http www idealibrary com on

droplet theory of low dimensional potts models formulates a generalisation of the droplet theory of ising systems to droplet systems containing more than two phases valid near one dimension and based on the configurational energy of surface tension thermal and magnetic exponents for these multi phase systems are compared with the results for a q state potts model in the external field the potts exponents are obtained using a migdal recursion formula and are shown to be of very similar structure

stratified symplectic spaces and reduction let m w be a hamiltonian g space with proper momentum map j m g it is well known that if zero is a regular value of j and g acts freely on the level set j 0 then the reduced space mo j 0 g is a symplectic manifold we show that if the regularity assumptions are dropped the space mo is a union of symplectic manifolds i e it is a stratified symplectic space arms et al 2 proved that mo possesses a natural poisson bracket using their result we study hamiltonian dynamics on the reduced space in particular we show that hamiltonian flows are strata preserving and give a recipe for lifting a reduced hamiltonian flow to the level set j 0 finally we give a detailed description of the stratification of mo and prove the existence of a connected

equivariant brst quantization and reducible symmetries working from first principles quantization of a class of hamiltonian systems with reducible symmetry is carried out by constructing first the appropriate reduced phase space and then the brst cohomology the constraints of this system correspond to a first class set for a group g and a second class set for a subgroup h the brst operator constructed is equivariant with respect to h using algebraic techniques analogous to those of equivariant de rham theory the brst operator is shown to correspond to that obtained by bv quantization of a class of systems with reducible symmetry the ghosts for ghosts correspond to the even degree two generators in the cartan model of equivariant cohomology as an example of the methods developed a topological model is described whose brst quantization relates to the equivariant cohomology of a manifold under a circle action

droplet theory in low dimensions ising systems in an ordering field the authors extend the microscopic droplet theory of ising systems developed recently to incorporate the effects of an ordering field the theory yields a free energy which is the solution of a renormalisation group equation describing droplet nesting and which has a full scaling form the behaviour near the coexistence curve is investigated and found to display the essential singularity suggested by primitive droplet models but with parameters renormalised in a physically intelligible way the droplet population function implied by the theory is parametrised in a simple way in space dimension d 2 to yield predictions for various thermodynamic properties including the equation of state which are found to be in fair accord with series based results the structure of the field dependent droplet number distributions is investigated and contrasted with the forms assumed in phenomenological droplet theories the domain of validity of the theory is assessed it is concluded that the theory fails to describe sufficiently large droplets in the presence of a finite field and is thus in principle trustworthy only in a region close to the coexistence curve

validity of classical nucleation theory for ising models while the classical nucleation theory cnt is widely used to predict the rate of first order phase transitions its validity has been questioned due to discrepancies with experiments we systematically test the individual components of cnt by computer simulations of the ising models and confirm its fundamental assumptions under a wide range of conditions h 0 01 text char21 0 13j t 0 44 text char21 0 84 t c in two dimensions and h 0 30 text char21 0 60j t 0 48 text char21 0 62 t c in three dimensions first cnt accurately predicts the nucleation rate if the correct droplet free energy is provided furthermore theoretical prediction of droplet free energy matches numerical results very well in the two dimensional 2d ising model if appropriate correction terms are added this establishes the 2d ising model as an important reference point where existing theories can predict nucleation rate accurately with no adjustable parameters

the mean size of ising clusters a confluent singularity analysis the authors re examine using a confluent singularity analysis existing low temperature series for the mean size of finite clusters for the pure spin 1 2 nearest neighbour ising model in two dimensions although the triangular lattice is problematical results for the honeycomb and square lattices may be interpreted as indicating a dominant exponent theta 1 87 or 0 04 consistent with the theoretical prediction theta gamma beta together with competing analytic and non analytic delta 1 1 35 or 0 25 correction to scaling terms

unconditional families in banach spaces it is shown that for every separable banach space x with non separable dual the space x contains an unconditional family of size x the proof is based on ramsey theory for trees and finite products of perfect sets of reals among its consequences it is proved that every dual banach space has a separable quotient

surface tension in potts models and percolation the kasteleyn fortuin relation 1969 is used to give a simple proof for the s state potts model of the relation beta sigma xi 1 between the correlation length in a particular direction on a planar lattice and the surface tension of an interface with corresponding orientation on the dual thus generalising a well known result for the ising model the relation is also used to give an interpretation of the surface tension in the percolation problem in general dimensions