conformal invariance and finite one dimensional quantum chains based on previous work of cardy 1984 the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions the method is illustrated in the case of the three and four state potts models where the anomalous dimensions of the para fermionic operators are found

effective critical exponents in two dimensional systems from conformal field theory abstract thermal and field perturbations away from the renormalization group fixed point are considered in 2d conformal field theory general expressions for the effective critical exponents and are obtained in terms of the central charge third moment of energy and spin correlation temperature and external field apparent spin dependence expressions for the effective critical exponents are given for a high spin system with only one fixed point these expression may be described as critical behavior and crossover phenomena for 2d systems away from the critical points

statistical analysis of airport network of china through the study of airport network of china anc composed of 128 airports nodes and 1165 flights edges we show the topological structure of anc conveys two characteristics of small worlds a short average path length 2 067 and a high degree of clustering 0 733 the cumulative degree distributions of both directed and undirected anc obey two regime power laws with different exponents i e the so called double pareto law in degrees and out degrees of each airport have positive correlations whereas the undirected degrees of adjacent airports have significant linear anticorrelations it is demonstrated both weekly and daily cumulative distributions of flight weights frequencies of anc have power law tails besides the weight of any given flight is proportional to the degrees of both airports at the two ends of that flight it is also shown the diameter of each subcluster consisting of an airport and all those airports to which it is linked is inversely proportional to its density of connectivity efficiency of anc and of its subclusters is measured through a simple definition in terms of that the efficiency of anc s subclusters increases as the density of connectivity does anc is found to have an efficiency of 0 484

finite size corrections and numerical calculations for long spin 1 2 heisenberg chains in the critical region leading and next to leading order finite size corrections to the ground and first excited states are calculated for the spin 1 2 anisotropic heisenberg model in the critical region the analytic results are compared to numerical data obtained for chains up to a length of n 1024 it is found that near the isotropic point the asymptotic region where the results obtained for n to infinity are applicable sets in at very large n values and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms even at large n 100 chain lengths

accelerated growth in outgoing links in evolving networks deterministic versus stochastic picture in several real world networks such as the internet world wide web etc the number of links grow in time in a nonlinear fashion we consider growing networks in which the number of outgoing links is a nonlinear function of time but new links between older nodes are forbidden the attachments are made using a preferential attachment scheme in the deterministic picture the number of outgoing links m t at any time t is taken as n t ensuremath theta where n t is the number of nodes present at that time the continuum theory predicts a power law decay of the degree distribution p k ensuremath propto k ensuremath 1 ensuremath 2 1 ensuremath ensuremath theta while the degree of the node introduced at time t i is given by k t i t t i ensuremath theta phantom rule 0 2em 0ex t t i 1 ensuremath theta 2 when the network is evolved till time t numerical results show a growth in the degree distribution for small k values at any nonzero ensuremath theta in the stochastic picture m t is a random variable as long as m t is independent of time the network shows a behavior similar to the barab asi albert ba model different results are obtained when m t is time dependent e g when m t follows a distribution p m ensuremath propto m ensuremath ensuremath lambda the behavior of p k changes significantly as ensuremath lambda is varied for ensuremath lambda g3 the network has a scale free distribution belonging to the ba class as predicted by the mean field theory for smaller values of ensuremath lambda it shows different behavior characteristic features of the clustering coefficients in both models have also been discussed

conformal anomaly and critical exponents of the spin 1 takhtajan babujian model the authors consider the critical behaviour of the spin 1 hamiltonian of the takhtajan babujian model the bethe ansatz equations for this antiferromagnet in a finite chain are investigated analytically and numerically the conformal anomaly and critical exponents are obtained by exploiting their relations with the eigenspectrum of the finite system the results strongly support the conjecture that the wess zumino witten non linear sigma model with topological charge k 2 is the underlying field theory for this statistical mechanics model

modeling the coevolution of topology and traffic on weighted technological networks for many technological networks the network structures and the traffic taking place on them mutually interact the demands of traffic increment spur the evolution and growth of the networks to maintain their normal and efficient functioning in parallel a change of the network structure leads to redistribution of the traffic in this paper we perform an extensive numerical and analytical study extending results of wang phys rev lett 94 188702 2005 by introducing a general strength coupling interaction driven by the traffic increment between any pair of vertices our model generates networks of scale free distributions of strength weight and degree in particular the obtained nonlinear correlation between vertex strength and degree and the disassortative property demonstrate that the model is capable of characterizing weighted technological networks moreover the generated graphs possess both dense clustering structures and an anticorrelation between vertex clustering and degree which are widely observed in real world networks the corresponding theoretical predictions are well consistent with simulation results

master equation analysis of accelerating networks in many real world networks the rates of node and link addition are time dependent this observation motivates the definition of accelerating networks there has been relatively little investigation of accelerating networks and previous efforts at analyzing their degree distributions have employed mean field techniques by contrast we show that it is possible to apply a master equation approach to such network development we provide full time dependent expressions for the evolution of the degree distributions for the canonical situations of random and preferential attachment in networks undergoing constant acceleration these results are in excellent agreement with results obtained from simulations we note that a growing nonequilibrium network undergoing constant acceleration with random attachment is equivalent to a classical random graph bridging the gap between nonequilibrium and classical equilibrium networks

finite lattice extrapolations for z3 and zs models a method is presented to accelerate the convergence of finite lattice sequences to their bulk limit the calculation of highly accurate estimates of the critical parameters of the bulk system is then possible applied to the hamiltonian version of the z3 model three state potts model in 1 1 dimensions these techniques yield estimates for the exponents gamma 1 444 or 0 0001 nu 0 8333 or 0 0003 and alpha 0 33 or 0 01 for the z5 model the presence of a kosterlitz thouless transition is confirmed

weighted self similar networks under preferential attachment abstract we introduce an abstract evolutionary formalism that generates weighted networks whose growth under stochastic preferential attachment triggers unrestricted weight rearrangements in existing links the class of resulting algorithms for different parameter values includes the barabasi albert and barrat barthelemy vespignani models as special cases we solve the recursions that describe the average growth to derive exact solutions for the expected degree and strength distribution the individual strength and weight development and the joint distribution of neighboring degrees we find that the network exhibits a particular form of self similarity namely every sufficiently interconnected node has on average the same constitution of small degree neighbors as any other node of large degree finally we suggest potential applications in several fields of interest

generating structured networks based on a weight dependent deactivation mechanism motivated by the degree dependent deactivation model generating networks with high clustering coefficient k klemm et al phys rev e 65 036123 2002 a weight dependent version is studied to model evolving networks the growth dynamics of the network is based on a naive weight driven deactivation mechanism which couples the establishment of new active vertices and the weights dynamical evolution both analytical solutions and numerical simulations show that the generated networks possess a high clustering coefficient larger than that for regular lattices of the same average connectivity weighted structured scale free networks are obtained as the deactivated vertex is target selected at each time step and weighted structured exponential networks are realized for the random selected case

operator content of the xxz chain the finite size scaling spectra of the xxz heisenberg chain are presented for even and odd numbers of sites respectively the operator content is given for free as well as for toroidal boundary conditions

local world evolving networks with tunable clustering abstract we propose an extended local world evolving network model including a triad formation tf step in the process of network evolution random fluctuation in the number of new edges is involved we derive analytical expressions for degree distribution clustering coefficient and average path length our model can unify the generic properties of real life networks scale free degree distribution high clustering and small inter node separation moreover in our model the clustering coefficient is tunable simply by changing the expected number of tf steps after a single local preferential attachment step

the operator content of the exactly integrable su n magnets the operator content of the exactly integrable models associated with the su n lie algebras with periodic boundaries are studied the authors results were obtained from a numerical and analytical analysis of the associated bethe ansatz equations the resulting spectra indicate that the ferromagnetic and antiferromagnetic models have different operator content for n 2 being realizations of distinct modular invariant solutions

on the critical behaviour of the anisotropic biquadratic spin 1 chain a study is made of the anisotropic biquadratic spin 1 hamiltonian introduced by batchelor et al 1990 this model can be represented as a sum of operators satisfying a temperley lieb algebra its critical behaviour is explored by using the relations between mass gap amplitudes and critical exponents predicted by conformal invariance the model like in the xxz chain is found to exhibit a line of continuously varying exponents by comparing its eigenspectrum with that of the xxz hamiltonian several exact values are predicted

weighted scale free networks in euclidean space using local selection rule received 23 july 2005 revised manuscript received 21 july 2006 published 22 september 2006a spatial scale free network is introduced and studied whose motivation originated in the growing internetas well as airport networks we argue that in these real world networks a new node necessarily selects one ofits neighboring local nodes for connection and is not controlled by preferential attachment as in the barabasi albert ba model this observation is mimicked in our model where the nodes pop up at randomly locatedpositions in the euclidean space and are connected to one end of the nearest link in spite of this crucialdifference it is observed that the leading behavior of our network is like that of the ba model de ning the linkweight as an algebraic power of its euclidean length the weight distribution and the nonlinear dependence ofthe nodal strength on the degree are analytically calculated it is claimed that a power law decay of the linkweights with time ensures such nonlinear behavior switching off the euclidean space from the same modelyields a much simpler de nition of the ba model where numerical effort grows linearly with

optimal quotients of modular jacobians let n be a positive integer and f a normalized newform of weight two on 0 n attached to f is an optimal quotient a f of the jacobian j 0 n we prove two theorems concerning such optimal quotients a let denote the algebra of endomorphisms of j 0 n generated by the hecke operators and let f denote the ideal of fusion of f in if f denotes the dual abelian variety to a f then the canonical polarization of j 0 n induces a polarization f f a f we show that there is an embedding ker f j 0 n f whose cokernel is supported at maximal ideals of for which j 0 n is not two dimensional b if n is prime let c denote the subgroup of j 0 n generated by the divisor 0 on x 0 n mazur has shown that c is equal to the full torsion subgroup of j 0 n and that specialization modulo n induces an isomorphism of c with the group of connected components j 0 n of the characteristic n fibre of the neron model of j 0 n we prove that analogous results hold for every optimal quotient of prime conductor thereby generalizing results of mestre and oesterle who treated the case of strong weil curves and confirming william stein s refined eisenstein conjecture the key idea in the proof of these two theorems is encapsulated in corollary 2 5 below which allows us to apply multiplicity one results in a novel way to the study of optimal quotients

effects of accelerating growth on the evolution of weighted complex networks many real systems possess accelerating statistics where the total number of edges grows faster than the network size in this paper we propose a simple weighted network model with accelerating growth we derive analytical expressions for the evolutions and distributions for strength degree and weight which are relevant to accelerating growth we also find that accelerating growth determines the clustering coefficient of the networks interestingly the distributions for strength degree and weight display a transition from scale free to exponential form when the parameter with respect to accelerating growth increases from a small to large value all the theoretical predictions are successfully contrasted with numerical simulations

continuously varying exponents and the value of the central charge the author shows that the conformal field theories describing two dimensional critical behaviour with continuously varying exponents must have central charge c 1 if a there are no conserved spin 2 currents other than the stress tensor and b the marginal operator responsible for the line of fixed points does not mix with other operators in such cases one may show the existence of a fixed line knowing only the four point function of the marginal operator the author applies this to the ashkin teller model and the xy model with fourfold symmetry breaking

finite size effects and 2 string deviations in the spin 1 xxz chains in an earlier work suzuki 2004 j phys a math gen 37 11957 proposed a set of nonlinear integral equations nlie to describe the excited state spectrum of the integrable spin 1 xxz chain in its repulsive regime in this paper we extend his equations for the attractive regime of the model and calculate analytically the conformal spectrum of the spin chain we also discuss the typical root configurations of the thermodynamic limit as well as the 2 string deviations of certain excited states of the model special objects appearing in the nlie are also treated with special care

conformal invariance and the xxz chain with arbitrary spin abstract the critical properties of the anistropic heisenberg chain or xxz model with arbitrary spins s are studied the eigenspectrum of these models for finite chain length is calculated by solving their associated bethe ansatz equations the operator content with an even and odd number of sites is obtained by exploring the consequences of conformal invariance the results indicate the existence of critical lines governed by conformal theories with central charge c 3s 1 s and c 1 with critical exponents varying continuously with the anisotropy like in the 8 vertex model

finite size corrections for ground states of the xxz heisenberg chain the method of de vega and woynarovitch 1985 is used to calculate finite size corrections to the ground state energy in different sectors for the xxz heisenberg chain finite size scaling amplitudes and correction to scaling exponents in the critical region are derived using conformal invariance a scaling dimension x pi gamma 2 pi is extracted corresponding to the electric field operator in the 8 vertex model this confirms a conjecture of baxter and kelland 1974 finite size scaling properties near the kosterlitz thouless critical point delta 1 are discussed

logarithmic corrections to finite size scaling in strips abstract the corrections to the finite size scaling behaviour of the eigenvalues of the transfer matrix of a critical theory defined on an infinitely long strip of finite width which occur when the hamiltonian contains a marginal operator are computed using conformal invariance they show a calculable universal logarthmic character for the four state potts model they agree with numerical data

analysis of the bethe ansatz equations for the anisotropic su 2 chain the bethe ansatz equations for the anisotropic spin s heisenberg chain are analysed numerically the position of the roots for the whole spectrum is calculated for the spin 1 model in a chain of width n 4 some states are presented which violate the normally accepted string hypothesis

power law accelerating growth complex networks with mixed attachment mechanisms abstract in this paper motivated by the thoughts and methods of the mixture of preferential and uniform attachments we extend the barabasi albert ba model and establish a network model with the power law accelerating growth and the mixture of the two attachment mechanisms in our model the number of edges generated by each newly introduced node is proportional to the power of 0 1 of time t i e m t by virtue of the continuum approach we have deduced the degree distribution p k t of our model with the extended power law form p k t a t k b t when the number of edges k generated by each new node is much greater than the value of b t the degree distribution p k t will converge to the power law form p k t a t k when k is much less than the value of b t the degree distribution p k t will converge to the exponential law form p k t a t b t e k b t by virtue of numerical simulations we also discuss the dependence of the degree distribution p k t on the model s parameters where t is considered as a constant in the simulations finally we investigate the possible application of our model in the spreading and evolution of epidemics in some real world systems

operator content of the three state potts quantum chain the authors compute the lowest excitations of the spectra of the three state potts quantum chain with periodic and twisted boundary conditions these spectra can be understood in terms of eighteen irreducible representations of the virasoro algebra with c 4 5

comment on critical behaviour of spin s heisenberg antiferromagnetic chains analytic and numerical results makes some observations on a recent paper by affleck et al ibid vol 22 p 511 1989 about the singlet excitation in the spin s 1 integrable model and logarithmic corrections for integrable spin models

accelerating hyperaccelerating and decelerating networks many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size in particular biological networks can display a quadratic growth in regulator number with genome size even while remaining sparsely connected these features are mutually incompatible in standard treatments of network theory which typically require that every new network node possesses at least one connection to model sparsely connected networks we generalize existing approaches and add each new node with a probabilistic number of links to generate either accelerating hyperaccelerating or even decelerating network statistics in different regimes under preferential attachment for example slowly accelerating networks display stationary scale free statistics relatively independent of network size while more rapidly accelerating networks display a transition from scale free to exponential statistics with network growth such transitions explain for instance the evolutionary record of single celled organisms which display strict size and complexity limits

the spin s xxz quantum chain with general toroidal boundary conditions the authors derive the operator content of the spin s xxz quantum chain with generalised toroidal boundary conditions compatible with the u 1 symmetry of the model these results are derived by solving numerically the associated bethe ansatz equations for finite chains and exploring the consequences of the conformal invariance of the infinite system they also show that as in the spin 1 2 case the conformal anomaly and dimensions of general extended su 2 algebras can be obtained from these spin s chains by choosing properly the coupling constant and the boundary condition

q deformations of the o 3 symmetric spin 1 heisenberg chain the authors present the general expression for the spin 1 heisenberg chain invariant under the uq so 3 quantum algebra several physical and mathematical implications are discussed

generalized local world models for weighted networks based on the weighted scale free network model proposed by barrat barth elemy and vespignani phys rev lett 92 228701 2004 and enlightened by our local world concept li and chen physica a 328 274 2003 we propose two generalized local world glw models for weighted complex networks theoretical analysis and numerical simulations show that the glw models generate weighted networks as a crossover between exponential and scale free weighted networks and exhibit an alteration from assortative networks to disassortative networks

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

excited state nonlinear integral equations for an integrable anisotropic spin 1 chain we propose a set of nonlinear integral equations to describe the excited states of an integrable the spin 1 chain with anisotropy the scaling dimensions evaluated numerically in previous studies are recovered analytically by using the equations this result may be relevant to the study of the supersymmetric sine gordon model

dynamic weight evolution network with preferential attachment abstract a dynamic weight evolution network with preferential attachment is introduced the network includes two significant characteristics i topological growth triggered by newly added node with m links at each time step each new edge carries an initial weight growing nonlinearly with time ii weight dynamics the weight between two existing nodes experiences increasing or decreasing in a nonlinear way by using continuum theory and mean field method we study the strength the degree the weight and their distributions we find that the distributions exhibit a power law feature in particular the relationship between the degree and the strength is nonlinear and the power law exponents of the three are the same all the theoretical predictions are successfully contrasted with numerical simulations

conformal invariance and correction to finite size scaling applications to the three state potts model corrections to finite size scaling are determined numerically for several levels of the three state potts quantum chain with various boundary conditions it is found that the leading correction term behaves like wo in the case of periodic and twisted boundary conditions the coefficients of the n o term are determined by the three point correlation functions of the conformal theory

the topology of an accelerated growth network we present and investigate a general nonlinear growth network model which incorporates accelerated growth of nodes and edges where the growth rates of edges and nodes are all time dependent power law functions the acceleration of edges determines the proportion of the internal edges to the external edges which play a key role influencing the structure of the network on the other hand the effects of the acceleration of nodes on the topology of the network are discussed in the present work this model predicts an observable two regime scale free degree distribution where the scaling exponents are 1 2 and 2 3 respectively the crossover point kcross of the degree distribution is adjusted by the growth rates of nodes and edges the nontrivial clustering coefficient and degree assortativity coefficient are relevant to the acceleration of nodes and edges

fractional strings hypothesis and non simple laced integrable models the author discusses the ground state and some elementary excitations of the bp non simple laced integrable models the zeros of the associated bethe ansatz equations are characterized by a special distribution in the complex plane which is different from the usual string hypothesis the introduction of this new solution makes it possible to calculate exactly various properties in the thermodynamic limit the finite size corrections to the eigenspectrum strongly suggest that the bp wess zumino witten novikov models are the underlying conformal field theory for these non simple laced models

modeling the evolution of weighted networks we present a general model for the growth of weighted networks in which the structural growth is coupled with the edges weight dynamical evolution the model is based on a simple weight driven dynamics and a weights reinforcement mechanism coupled to the local network growth that coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real world networks the model generates weighted graphs exhibiting the statistical properties observed in several real world systems in particular the model yields a nontrivial time evolution of vertices properties and scale free behavior with exponents depending on the microscopic parameters characterizing the coupling rules very interestingly the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices degree

the phase boundary in dilute and random ising and potts ferromagnets the authors present an approach to dilute ising and potts models based on the fortuin kasteleyn random cluster representation which is simultaneously rigorous intuitive and surprisingly simple their analysis yields with no dimensional restrictions or other caveats the following asymptotic form of the phase boundary for the regular dilute model in which bonds have constant ferromagnetic coupling j with probability p and are vacant with probability 1 p the critical temperature scales as exp j ktc p approximately mod p pc mod implying that the crossover exponent is phi 1 if the constant couplings are replaced by a distribution f j with mass near j 0 quite different crossover behaviour is observed for example if f j approximately jalpha then for p near pc tc p approximately mod p pc mod 1 alpha

analytical and non analytical corrections to finite size scaling using conformal invariance the author calculates finite size corrections to the scaled spectra of one dimensional quantum chains at the critical point an explicit application to the ising and three state potts model gives good agreement with analytical and numerical results respectively

weight driven growing networks we study growing networks in which each link carries a certain weight randomly assigned at birth and fixed thereafter the weight of a node is defined as the sum of the weights of the links attached to the node and the network grows via the simplest weight driven rule a newly added node is connected to an already existing node with the probability which is proportional to the weight of that node we show that the node weight distribution n w has a universal tail that is it is independent of the link weight distribution n w approximately w 3 as w infinity results are particularly neat for the exponential link weight distribution when n w is algebraic over the entire weight range

canonical periods and congruence formulae the purpose of this article is to show how congruences between the fourier coefficients of hecke eigenforms give rise to corresponding congruences between the algebraic parts of the critical values of the associated l functions this study was initiated by b mazur in his fundamental work on the eisenstein ideal see maz77 and maz79 where it was made clear that congruences for analytic l values were closely related to the integral structure of certain hecke rings and cohomology groups the results of maz79 also showed that congruences were useful in the study of nonvanishing of l functions this idea was then further developed by stevens ste82 and rubin wiles rw82 the work of rubin and wiles in particular used congruences to study the behavior of elliptic curves in towers of cyclotomic fields a key ingredient here was a theorem of washington which states roughly that almost l values in certain families are nonzero modulo p this theme has recently been taken up again in the work of ono skinner osa osb james jam and kohnen koh97 while the earlier history was primarily concerned with cyclotomic twists the current emphasis is on families of twists by quadratic characters here one wants quantitative estimates for the number of quadratic twists of a given modular form which have nonvanishing l function at s 1 we continue this trend in the present work by using our general results to obtain a strong nonvanishing theorem for the quadratic twists of modular elliptic curves with rational points of order three this generalizes a beautiful example due to kevin james and provides new evidence for a conjecture of goldfeld gol79 it should however be pointed out that even the study of quadratic twists may be traced back to mazur the reader is urged to look at pages 212 213 of maz79 and especially at the footnote at the bottom of page 213 the theorems of davenport heilbronn dh71 and washington was78 which are crucial in this paper are both mentioned in mazur s article we want to begin by discussing the congruences that lie at the heart of this article thus let f anq n be an elliptic modular cuspform of level m and weight k 2 assume that f is a simultaneous eigenform for all the hecke operators and that a1 f 1 the l function associated to f is defined by the dirichlet series l s f ann s which converges for the real part of s sufficiently large and has analytic continuation to s c a fundamental theorem of shimura shi76 states that l s f enjoys the following algebraicity property

operator content of the fusion cyclic solid on solid model the fusion model of the l state cyclic solid on solid csos model is considered at criticality each zl charge sector of the fusion csos model is related to a sum of total spin sectors of the fusion vertex model with a seam on which the vertex weights are modified by a phase factor the latter in turn becomes the higher spin xxz quantum chain with a twisted boundary condition in the extremely anisotropic limit using the known operator content of the higher spin xxz chain the authors deduce that of the fusion csos model the modular invariant partition function of the fusion csos at fusion level k is a sum of products of the z k parafermionic and free boson sectors with the effective coupling g l2 k lambda pi for l odd and g l2 1 k lambda pi 4 for l even where lambda is the crossing parameter where l is odd and a multiple of k or when l 2 is a multiple of k for l even the modular invariant partition function becomes a simple product of the z k parafermionic and the gaussian partition function

an analytic treatment of finite size corrections in the spin 1 antiferromagnetic xxz chain it is known that the standard method for calculating finite size corrections in bethe ansatz solvable systems is not applicable to the takhtajan babujian model and its anisotropic xxz generalisation the authors develop a new analytic method explicitly avoiding root densities and associated problems nonlinear integral equations are derived whose solutions yield the correct central charges c 1 and c 3 2 for the spin 1 2 and spin 1 xxz chains respectively in the spin 1 case the authors obtain as a by product the finite size deviation of the bethe ansatz roots from the 2 string formation

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

conformal invariance and critical exponents of the takhtajan babujian models the authors are concerned with the critical properties of antiferromagnetic takhtajan babujian models with spin s 1 3 2 and 2 the leading eigenenergies of this hamiltonian in a finite chain are calculated by investigating numerically and analytically the bethe ansatz equations for the finite system the critical exponents and the conformal anomaly are obtained from their relations with the eigenspectrum of the finite hamiltonian the appearance of logarithmic corrections produces poor estimates however a combination of analytical and numerical methods produces very good estimates their results strongly support the conjecture that the wess zumino witten novikov non linear sigma models with topological charge k 2s are the underlying field theories for these spin s statistical mechanics models

finite size effects in the integrable xxz heisenberg model with arbitrary spin the finite size effects in the spectrum of the integrable xxz heisenberg chain with arbitrary spin s are studied analytically on the basis of the string hypothesis for bound states and numerically by solving the associated bethe ansatz equations the finite size corrections to the spectrum and to the low temperature behaviour of the free energy are found to be similar to the universal predictions for conformally invariant theories although the model is in general not lorentz invariant since it can have an arbitrary number of branches for low energy excitations with different fermi velocities depending on the value of s and the anisotropy parameter gamma

high temperature expansion for a chain model we consider an arbitrary translationally invariant chain model with nearest neighbors interaction and satisfying periodic boundary condition the approach developed here allows a thermodynamic description of the chain model directly in terms of grand potential per site this thermodynamic function is derived from an auxiliary function constructed only from open connected subchains in order to exemplify its application and how this approach works we consider the heisenberg xxz model we obtain the coefficients of the high temperature expansion of the free energy per site of the model up to third order

conformal invariance and the operator content of the xxz model with arbitrary spin the authors are concerned with the critical properties of the anisotropic heisenberg chain or xxz model with arbitrary integer or half integer spin the eigenspectra of these hamiltonians with periodic boundaries are calculated for finite chains by solving numerically their associated bethe ansatz equations the resulting spectra are found to be in accord with the predictions of conformal invariance and the operator content is identified for lattices with an even and odd number of sites the results for spin 1 and spin 3 2 indicate that the conformal anomaly c for these models in the gapless regime has the value c 3s 1 s independent of the anisotropy and the exponents vary continuously with the anisotropy as in the eight vertex model the operator content of these models indicate that the underlying field theory governing these critical spin s models is described by composite fields formed by the product of gaussian and z n fields with n 2s finally some of the irrelevant operators which produce the leading finite size corrections of the eigenenergies are identified

conformal invariance and line defects in the two dimensional ising model the quantum ising chain with p equidistant defects is studied the exact form of the hamiltonian is found for an infinite number of sites using conformal invariance generalised corner exponents are computed and found to depend continuously on the defect strengths realisations of extended conformal algebras in the hamiltonian spectrum are obtained