on the existence of local observables in theories with a factorizing s matrix the scaling limit of the two dimensional ising model above the critical temperature is considered as an example for relativistic quantum theories on two dimensional minkowski space exhibiting a factorizing s matrix in this model a recently proposed criterion for the existence of local quantum field theories with a prescribed factorizing scattering matrix is verified thereby establishing a new constructive approach to two dimensional quantum field theory in a particular example the existence proof is accomplished by analysing the nuclearity properties of certain specific subsets of fermionic fock spaces and yields as a byproduct also a verification of the energy nuclearity condition of buchholz and wichmann in models of free fermions in four spacetime dimensions

short time dynamics and magnetic critical behavior of the two dimensional random bond potts model the critical behavior in the short time dynamics for the random bond potts ferromagnet in two dimensions is investigated by short time dynamic monte carlo simulations the numerical calculations show that this dynamic approach can be applied efficiently to study the scaling characteristic which is used to estimate the critical exponents straight theta beta nu and z for quenched disordered systems from the power law behavior of the kth moments of magnetization

non equilibrium critical relaxation of the three dimensional ising model abstract the non equilibrium relaxation process at the critical point is studied using monte carlo simulation for the ferromagnetic ising model on a cubic lattice it was observed that the time dependent magnetization decayed following a power law t from the all up initial condition three kinds of single spin flip dynamics were studied for several lattices up to 1536 3 the system size dependences are also studied the value of was estimated to be 0 250 2 this value of leads to the estimation of the dynamical exponent z to be 2 06 2 if we assume z where and denote the critical exponents for spontaneous magnetization and correlation length in equilibrium state respectively and 0 515 the result of the non equilibrium relaxation in the ordered phase is also given

quadratic forms of signature 2 2 and eigenvalue spacings on rectangular 2 tori the oppenheim conjecture proved by margulis mar1 see also mar2 asserts that for a nondegenerate indefinite irrational quadratic form q in n 3 variables the set q zn is dense in emm where we used the lower bounds established in dm a quantitative version of the conjecture was established namely let be a continuous positive function on the sphere v rn v 1 and let v rn v v v we denote by t the dilate of by t for an indefinite quadratic form q in n variables let nq a b t denote the cardinality of the set

string localized quantum fields and modular localization we study free covariant quantum bose fields that are associated with irreducible representations of the poincare group and localized in semi infinite strings extending to spacelike infinity among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point like localized fields for the massive representations and the massless representations of finite helicity all string localized free fields can be written as an integral along the string of point localized tensor or spinor fields as a special case we discuss the string localized vector fields associated with the point like electromagnetic field and their relation to the axial gauge condition in the usual setting

deformations of quantum field theories and integrable models deformations of quantum field theories which preserve poincare covariance and localization in wedges are a novel tool in the analysis and construction of model theories here a general scenario for such deformations is discussed and an infinite class of explicit examples is constructed on the borchers uhlmann algebra underlying wightman quantum field theory these deformations exist independently of the space time dimension and contain the recently studied warped convolution deformation as a special case in the special case of two dimensional minkowski space they can be used to deform free field theories to integrable models with non trivial s matrix

quantitative version of the oppenheim conjecture for inhomogeneous quadratic forms a quantitative version of the oppenheim conjecture for inhomogeneous quadratic forms is proved we also give an application to eigenvalue spacing on flat 2 tori with aharonov bohm flux

string and brane localized causal fields in a strongly nonlocal model we study a weakly local but nonlocal model in spacetime dimension d 2 and prove that it is maximally nonlocal in a certain specific quantitative sense nevertheless depending on the number of dimensions d it has string localized or brane localized operators which commute at spatial distances in two spacetime dimensions the model even comprises a covariant and local subnet of operators localized in bounded subsets of minkowski space which has a nontrivial scattering matrix the model thus exemplifies the algebraic construction of local operators from algebras associated with nonlocal fields

statistical properties of spectral fluctuations for a quantum system with infinitely many components extending the idea formulated in makino phys rev e 67 066205 2003 that is based on the berry robnik approach m v berry and m robnik j phys a 17 2413 1984 we investigate the statistical properties of a two point spectral correlation for a classically integrable quantum system the eigenenergy sequence of this system is regarded as a superposition of infinitely many independent components in the semiclassical limit we derive the level number variance lnv in the limit of infinitely many components and discuss its deviations from poisson statistics the slope of the limiting lnv is found to be larger than that of poisson statistics when the individual components have a certain accumulation this property agrees with the result from the semiclassical periodic orbit theory that is applied to a system with degenerate torus actions d biswas m azam and s v lawande phys rev a 43 5694 1991

non equilibrium relaxation and interface energy of the ising model abstract from the non equilibrium critical relaxation study of the two dimensional ising model the dynamical critical exponent z is estimated to be 2 165 0 010 for this model the relaxation in the ordered phase of this model is consistent with exp t behavior the interface energy of the three dimensional ising model is studied and the critical exponent of the correlation length and the critical amplitude of the surface tension 0 are estimated to be 0 6250 0 0025 and 1 42 0 04 respectively a dynamic monte carlo renormalization group method is successfully applied to the equilibrium properties of the three dimensional ising model

passive states for essential observers the aim of this note is to present a unified approach to the results given by borchers and buchholz global properties of vacuum states in de sitter space ann inst henri poincare sect a 70 23 40 1999 and by buchholz and summers stable quantum systems in anti de sitter space causality independence and spectral properties j math phys 45 4810 4831 2004 which also covers examples of models not presented in these two papers e g d dimensional minkowski space time for d 3 assuming that a state is passive for an observer traveling along certain essential worldlines we show that this state is invariant under the isometry group is a temperature equilibrium state for the observer at a temperature uniquely determined by the structure constants of the lie algebra involved and fulfills a variant of the reeh schlieder property also the modular objects associated with such a state and the observable algebra of an observer are computed and a version of weak locality is examined

dynamical rushbrooke s inequality for nonequilibrium relaxation process an inequality for dynamic critical exponents is proved for relaxation processes of arbitrary magnetic systems this is a dynamical extension of rushbrooke s inequality it can be applied to any continuous transition systems with various dynamics the relation is demonstrated on the result of nonequilibrium relaxation analysis of fluctuations applied to the three dimensional ferromagnetic ising model

multicritical dynamics for the j ising model exact dynamical properties are discussed for the j ising model around the multicritical point mcp it is found that the relation of relaxations between the non equilibrium remanent magnetization m t and the equilibrium autocorrelation function q t at the mcp is different from that at the pure critical point the dynamic critical exponent for the ferromagnetic ordering defined by and that for the spin glass ordering defined by become identical at the mcp accurate numerical calculations for them are performed in two and three dimensions using the non equilibrium relaxation analysis the mcp is located at and the exponent is estimated as for the square lattice they are estimated as and for the simple cubic lattice

nonequilibrium relaxation study on spin glass model ferromagnetic fm transition point and universality class of the j ising model on cubic lattice are studied by computer simulation using the nonequilibrium relaxation ner method at fm bond density p between multicritical one pmc and 1 static exponents take universal values which are different from those of p 1 or p pmc and they are consistent with the values of the random fixed point and of the simulations and experiments for diluted ising systems the dynamical exponent however seems to depend on p and not to be universal although it may be due to finite time correction the estimation of pmc on square lattice is also refined to be 0 8894 9 which is consistent with the nishimori and nemoto s conjecture 0 889972

on raghunathan s measure conjecture this paper represents the last in our three part series on raghunathan s measure conjecture see r1 r2 for parts i and ii more specifically let g be a real lie group all groups in this paper are assumed to be second countable with the lie algebra r a discrete subgroup of g and ir g r g the projection lwg rg the group g acts by right translations on r g x x g x e r g g e g let gt be a borel probability measure on r g define

self averaging distribution of pseudocritical temperatures and finite size scaling in critical disordered systems we evaluate by monte carlo simulations various singular thermodynamic quantities x for ensembles of quenched random ising and ashkin teller models the measurements are taken at t c and we study how the distributions p x and in particular their relative squared width r x over the ensemble depend on the system size l the ashkin teller model was studied in the regime where bond randomness is irrelevant and we found weak self averaging r x ensuremath sim l ensuremath alpha ensuremath nu ensuremath rightarrow 0 where ensuremath alpha l0 and ensuremath nu are the exponents of the pure model fixed point governing the transition for the site dilute ising model on a cubic lattice known to be governed by a random fixed point we find that r x tends to a constant as predicted by aharony and harris we tested whether this constant is universal however this constant is different for canonical and grand canonical disorder we identify the pseudocritical temperature of each sample i t c i l as the temperature at which the susceptibility reaches its maximal value ensuremath chi mathrm max the distribution of these sample dependent t c i l was investigated we found that its variance scales as ensuremath delta t c l 2 ensuremath sim l ensuremath 2 ensuremath nu our previously proposed finite size scaling ansatz for disordered systems was tested and found to hold we did observe deviations from a single function which imply that sample dependent scaling functions are needed these deviations are however relatively small and hence to obtain a fixed statistical error it may be more computationally efficient to measure ensuremath chi mathrm max than the commonly used ensuremath chi t c ensuremath infty

construction of quantum field theories with factorizing s matrices the subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two dimensional minkowski space employing the algebraic framework of quantum field theory it is shown under which conditions an algebra of observables localized in a wedge shaped region of spacetime can be used to construct model theories a crucial input in this context is the modular nuclearity condition for wedge algebras which implies the existence of local observables as an application of the new method a rigorous construction of a large family of models with factorizing s matrices is obtained in an inverse scattering approach a given factorizing scattering operator is used to define certain semi localized wightman fields associated to it with the help of these fields a wedge algebra can be defined which determines the local observable content of a well defined quantum field theory in this approach the modular nuclearity condition translates to certain analyticity and boundedness conditions on the formfactors of wedge local observables these conditions are shown to hold for a large class of underlying s matrices including the scattering operators of the sinh gordon model and the scaling ising model as special examples the so constructed models are investigated with respect to their scattering properties they are shown to solve the inverse scattering problem for the underlying s matrices and a proof of asymptotic completeness for these models is given

localized eigenfunctions in seba billiards we describe some new families of quasimodes for the laplacian perturbed by the addition of a potential formally described by a dirac delta function as an application we find under some additional hypotheses on the spectrum subsequences of eigenfunctions of seba billiards that localize around a pair of unperturbed eigenfunctions