the yang lee edge singularity in spin models on connected and non connected rings renormalization group arguments based on a 3 field theory lead us to expect a certain universal behavior for the density of partition function zeros in spin models with short range interaction such universality has been tested analytically and numerically in different d 1 and higher dimensional spin models in d 1 one finds usually the critical exponent 1 2 recently we have shown in the d 1 blume emery griffiths beg model on a periodic static lattice one ring that a new critical behavior with 2 3 can arise if we have a triple degeneracy of the transfer matrix eigenvalues here we define the d 1 beg model on a dynamic lattice consisting of connected and non connected rings non periodic lattice and check numerically that also in this case we have mostly 1 2 while the new value 2 3 can arise under the same conditions of the static lattice triple degeneracy which is a strong check of universality of the new value of we also show that although such conditions are necessary they are not sufficient to guarantee the new critical behavior

the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

spiral arc spline approximation to a planar spiral a biarc is a one parameter family of g 1 curves that can satisfy g 1 hermite data at two points an arc spline approximation to a smooth planar curve can be found by reading g 1 hermite data from the curve and tting a biarc between each pair of data points the resulting collection of biarcs forms a g 1 arc spline that interpolates the entire set of g 1 hermite data if the smooth curve is a spiral it is desirable that the arc spline approximation also be a spiral several methods are described for choosing the free parameters of the biarcs so that the arc spline approximation to a smooth spiral is a spiral c 1999 elsevier science b v all rights reserved

non borel summable φ4 theory in zero dimension a toy model for testing numerical and analytical methods the exact analytical solution for the generating functional of the zero dimensional 4 theory with degenerate minima is obtained in the whole complex coupling parameter plane for testing purposes the efficiency and precision of different computing tools proposed in non borel summable field theories to obtain approximate solutions in both perturbative and nonperturbative regimes are analyzed furthermore a new resummation approach is proposed in order to successfully deal with factorially divergent series it provides a representation of the generating function in terms of an unambiguously defined laplace borel integral on the other hand a recent approach called the generalized borel transform is shown to be an accurate and robust technique to capture non perturbative contributions in the coupling parameter an extension of this approach to path integrals is proposed

exact results for the zeros of the partition function of the potts model on finite lattices the yang lee zeros of the q state potts model are investigated in one two and three dimensions analytical results derived from the transfer matrix for the one dimensional model reveal a systematic behavior of the locus of zeros as a function of q for 1 2 they lie outside the unit circle for finite temperature in the special case q 2 the zeros lie exactly on the unit circle as proved by lee and yang in two and three dimensions the zeros are calculated numerically and behave in the same way results are also presented for the critical line of the potts model in an external field as determined from the zeros of the partition function in the complex temperature plane

ground state entropy of the potts antiferromagnet on strips of the square lattice abstract we present exact solutions for the zero temperature partition function chromatic polynomial p and the ground state degeneracy per site w exponent of the ground state entropy for the q state potts antiferromagnet on strips of the square lattice of width ly vertices and arbitrarily great length lx vertices the specific solutions are for a ly 4 fbcy pbcx cyclic b ly 4 fbcy tpbcx mobius c ly 5 6 pbcy fbcx cylindrical and d l y 5 fbc y fbc x open where fbc pbc and tpbc denote free periodic and twisted periodic boundary conditions respectively in the lx limit of each strip we discuss the analytic structure of w in the complex q plane the respective w functions are evaluated numerically for various values of q several inferences are presented for the chromatic polynomials and analytic structure of w for lattice strips with arbitrarily great ly the absence of a nonpathological lx limit for real nonintegral q in the interval 0 0 for strips of the square triangular lattice is discussed

quenched random graphs spin models on quenched random graphs are related to many important optimization problems we give a new derivation of their mean field equations that elucidates the role of the natural order parameter in these models

approximation of a planar cubic bezier spiral by circular arcs a planar cubic bezier curve that is a spiral i e its curvature varies monotonically does not have internal cusps loops and inflection points it is suitable as a design tool for applications in which fair curves are important since it is polynomial it can be conveniently incorporated in cad systems that are based on b splines bezier curves or nurbs when machining objects it is desirable that as much as possible of a curved toolpath be approximated by a sequence of circular arcs rather than straight line segments such an arc spline approximation of a planar cubic bezier spiral is presented

capacity planning for phased implementation of flexible manufacturing systems under budget restrictions we consider a problem of gradually replacing conventional dedicated machines with flexible manufacturing modules fmms under budget restrictions over a finite planning horizon assuming that dedicated machines cannot be purchased during the planning horizon and acquired fmms are kept until the end of the horizon in the problem a replacement schedule is to be determined and operations are to be assigned to the fmms or the dedicated machines with the objective of minimizing the sum of discounted costs of acquisition and operation of fmms and operation costs of conventional dedicated machines in this research the problem is formulated as a mixed integer linear program and solved by a lagrangean relaxation approach a subgradient optimization method is employed to obtain lower bounds of solutions and a multiplier adjustment method is devised to improve the lower bounds we develop a linear programming based lagrangean heuristic algorithm to find a good feasible solution of the original problem in a reasonable amount of computation time the algorithm is tested on randomly generated test problems and the results are reported

resource constrained management of heterogeneous assets with stochastic deterioration we consider a collection of heterogeneous assets which exhibit independent stochastic behavior but are economically interdependent due to resource constraints on management decisions we represent the collection of assets as a network of nonhomogeneous markov decision processes linked by side constraints to facilitate a procedure for obtaining nonrandomized decision policies we express the resource limitations as integrated chance constraints and relax them into the objective function within a lagrangian penalty term we utilize subgradient optimization to establish upper bounds and a greedy randomized lagrangian repair heuristic to obtain feasible solutions we empirically validate the tightness of these a posteriori upper and lower bounds with computational experiments on a pair of applications for pavement maintenance we examine the effect that the reward structure of each constituent mdp has on the maintenance policy in the presence of budget constraints for equipment replacement we consider constraints on two resource types

chromatic polynomials for j h i strip graphs and their asymptotic limits abstract we calculate the chromatic polynomials p for n vertex strip graphs of the form j l 1 m h i where j and i are various subgraphs on the left and right ends of the strip whose bulk is comprised of m fold repetitions of a subgraph h the strips have free boundary conditions in the longitudinal direction and free or periodic boundary conditions in the transverse direction this extends our earlier calculations for strip graphs of the form l 1 m h i we use a generating function method from these results we compute the asymptotic limiting function w lim n p 1 n for q z this has physical significance as the ground state degeneracy per site exponent of the ground state entropy of the q state potts antiferromagnet on the given strip in the complex q plane w is an analytic function except on a certain continuous locus b in contrast to the l 1 m h i strip graphs where b i is independent of i and ii consists of arcs and possible line segments that do not enclose any regions in the q plane we find that for some j l 1 m h i strip graphs b i does depend on i and j and ii can enclose regions in the q plane our study elucidates the effects of different end subgraphs i and j and of boundary conditions on the infinite length limit of the strip graphs

asymptotic limits and zeros of chromatic polynomials and ground state entropy of potts antiferromagnets we study the asymptotic limiting function w g q lim n to infty p g q 1 n where p g q is the chromatic polynomial for a graph g with n vertices we first discuss a subtlety in the definition of w g q resulting from the fact that at certain special points q s the following limits do not commute lim n to infty lim q to q s p g q 1 n ne lim q to q s lim n to infty p g q 1 n we then present exact calculations of w g q and determine the corresponding analytic structure in the complex q plane for a number of families of graphs g including circuits wheels biwheels bipyramids and cyclic and twisted ladders we study the zeros of the corresponding chromatic polynomials and prove a theorem that for certain families of graphs all but a finite number of the zeros lie exactly on a unit circle whose position depends on the family using the connection of p g q with the zero temperature potts antiferromagnet we derive a theorem concerning the maximal finite real point of non analyticity in w g q denoted q c and apply this theorem to deduce that q c sq 3 and q c hc 3 sqrt 5 2 for the square and honeycomb lattices finally numerical calculations of w hc q and w sq q are presented and compared with series expansions and bounds

approximating smooth planar curves by arc splines when a smooth curve is used to describe the path of a computer controlled cutting machine the path is usually approximated by many straight line segments it is preferable to describe the cutting path as an arc spline a tangent continuous piecewise curve made of circular arcs and straight line segments this paper presents an algorithm for finding an arbitrarily close arc spline approximation of a smooth curve

application of statistical mechanics to np complete problems in combinatorial optimisation recently developed techniques of the statistical mechanics of random systems are applied to the graph partitioning problem the averaged cost function is calculated and agrees well with numerical results the problem bears close resemblance to that of spin glasses the authors find a spin glass transition in the system and the low temperature phase space has an ultrametric structure this sheds light on the nature of hard computation problems

the partition function zeros in the one dimensional q state potts model the zeros of the partition function in the one dimensional q state potts model with arbitrary and continuous q or 0 have been studied using a transfer matrix the location of zeros and the yang lee edge singularity have been analysed and two different regimes corresponding to q 1 and q 1 have been observed a duality relation has also been derived which relates the zeros in the complex field plane to those in the complex temperature plane

thin fisher zeros various authors have suggested that the loci of partition function zeros can profitably be regarded as phase boundaries in the complex temperature or field planes we obtain the fisher zeros for ising and potts models on non planar thin regular random graphs using this approach and note that the locus of fisher zeros on a bethe lattice is identical to the corresponding random graph since the number of states q appears as a parameter in the potts solution the limiting locus of chromatic zeros is also accessible

chaotic behavior of renormalization flow in a complex magnetic field it is demonstrated that decimation of the one dimensional ising model with periodic boundary conditions results in a nonlinear renormalization transformation for the couplings which can lead to chaotic behavior when the couplings are complex the recursion relation for the couplings under decimation is equivalent to the logistic map or more generally the mandelbrot map in particular an imaginary external magnetic field can give chaotic trajectories in the space of couplings the magnitude of the field must be greater than a minimum value which tends to zero as the critical point t 0 is approached leading to a gap equation and an associated critical exponent which are identical to those of the lee yang edge singularity in one dimension

circular spline fitting using an evolution process we propose a new method to approximate a given set of ordered data points by a spatial circular spline curve at first an initial circular spline curve is generated by biarc interpolation then an evolution process based on a least squares approximation is applied to the curve during the evolution process the circular spline curve converges dynamically to a stable shape our method does not need any tangent information during the evolution process the number of arcs is automatically adapted to the data such that the final curve contains as few arc arcs as possible we prove that the evolution process is equivalent to a gauss newton type method

abstract splines in krein spaces abstract we present generalizations to krein spaces of the abstract interpolation and smoothing problems proposed by atteia in hilbert spaces given a krein space k and hilbert spaces h and e bounded surjective operators t h k and v h e 0 and a fixed z 0 e we study the existence of solutions of the problems argmin t x t x k v x z 0 and argmin t x t x k v x z 0 e 2 x h

the yang lee edge singularity on feynman diagrams we investigate the yang lee edge singularity on non planar random graphs which we consider as the feynman diagrams of various d 0 field theories in order to determine the value of the edge exponent we consider the hard dimer model on and random graphs to test the universality of the exponent with respect to coordination number and the ising model in an external field to test its temperature independence the results here for generic thin random graphs provide an interesting counterpoint to the discussion by staudacher of these models on planar random graphs

potts models on feynman diagrams we investigate numerically and analytically potts models on thin random graphs generic feynman diagrams using the idea that such models may be expressed as the limit of a matrix model the thin random graphs in this limit are locally tree like in distinction to the fat random graphs that appear in the planar feynman diagram limit more familiar from discretized models of two dimensional gravity the interest of the thin graphs is that they give mean field theory behaviour for spin models living on them without infinite range interactions or the boundary problems of genuine tree like structures such as the bethe lattice q state potts models display a first order transition in the mean field for q 2 so the thin graph potts models provide a useful test case for exploring discontinuous transitions in mean field theories in which many quantities can be calculated explicitly in the saddle point approximation such discontinuous transitions also appear in multiple ising models on thin graphs and may have implications for the use of the replica trick in spin glass models on random graphs

a note on the non perturbative zero dimensional λϕ4 model abstract we exhibit the partition function of the zero dimensional 4 model as a simple exact expression in terms of the macdonald function for re 0 then by analytic continuation we obtain an expression defined in the complex coupling constant plane for arg consequently the partition function understood as an analytic continuation is defined for all values of except for a branch cut along the real negative axis this shows that at least in zero dimension the partition function can be defined for negative coupling constant where the integral is formally divergent provided it has a non vanishing imaginary part we also evaluate the partition function on perturbative grounds using the borel summation technique and we found that in the common domain of validity for re 0 it coincides precisely with the exact expression furthermore a connection between the non perturbative zero dimensional solution and the ultralocal 4 model in arbitrary dimension d is presented

partition function zeros of the one dimensional blume capel model in transfer matrix formalism zeros of the partition function of the one dimensional ferromagnetic and antiferromagnetic blume capel models have been studied by using the transfer matrix method in the thermodynamic limit and for finite size chains the equation for the distribution of zeros of the partition function in the thermodynamic limit is derived the distribution of the yang lee and fisher zeros are studied for a variety of values of the parameters of the model densities of the yang lee and fisher zeros are investigated and a singular behavior of the corresponding densities of zeros at the edge points is shown the edge singularity exponents are calculated analytically for the densities of the yang lee and fisher zeros it is found that for both cases edge singularity exponents are universal and equal to sigma 1 2

ground state entropy of the potts antiferromagnet on cyclic strip graphs we present exact calculations of the zero temperature partition function chromatic polynomial and the exponent of the ground state entropy s0 for the q state potts antiferromagnet on families of cyclic and twisted cyclic mobius strip graphs composed of p sided polygons our results suggest a general rule concerning the maximal region in the complex q plane to which one can analytically continue from the physical interval where s0 0 the chromatic zeros and their accumulation set exhibit the rather unusual property of including support for re q 0 and provide further evidence for a relevant conjecture

the partition function zeros of the anisotropic ising model with multisite interactions on a zigzag ladder abstract it is shown that the spin 1 2 anisotropic ising model with multisite interactions on a zigzag ladder may be mapped into the one dimensional spin 1 2 axial next nearest neighbor ising annni model with multisite interactions the partition function zeros of the annni model with multisite interactions are investigated a comprehensive analysis of the partition function zeros of the annni model with and without three site interactions on a zigzag ladder is done using the transfer matrix method analytical equations for the distribution of the partition function zeros in the complex magnetic field yang lee zeros and temperature fisher zeros planes are derived the yang lee and fisher zeros distributions are studied numerically for a variety of values of the model parameters the densities of the yang lee and fisher zeros are studied and the corresponding edge singularity exponents are calculated it is shown that the introduction of three site interaction terms in the annni model leads to a simpler distribution of the partition function zeros for example the yang lee zeros tend to a circular distribution when increasing by modulus the three site interactions term coefficient it is found that the yang lee and fisher edge singularity exponents are universal and equal to each other 1 2

an arc spline approximation to a clothoid the clothoid is a spiral used in highway and railway route design clothoids are transcendental functions and so have been approximated by polynomials by power series and continued fractions and by rational functions here the clothoid is approximated by an arc spline the chief advantage in doing so is that arc splines are very easy to lay out and to offset examples show that the approximation is of extremely high accuracy it is proved that if the arc spline has n arcs then the error in the approximation is of order o 1 n2

geometric hermite interpolation with tschirnhausen cubics explicit formulae are found that give the unique tschirnhausen cubic that solves a geometric hermite interpolation problem that solution is used to create a planar g1 spline by joining segments of tschirnhausen cubics if the geometric hermite data is from a smooth function the tschirnhausen cubic approximates the smooth function the error in the approximation of a short segment of length h can be expressed as a power series in h the error is o h4 and the coefficient of the leading term is found

complex temperature properties of the two dimensional ising model for nonzero magnetic field we study the complex temperature phase diagram of the square lattice ising model for nonzero external magnetic field h i e for 0 le mu le infty where mu e 2 beta h we also carry out a similar analysis for infty le mu le 0 the results for the interval 1 le mu le 1 provide a new way of continuously connecting the two known exact solutions of this model viz at mu 1 onsager yang and mu 1 lee and yang our methods include calculations of complex temperature zeros of the partition function and analysis of low temperature series expansions for real nonzero h the inner branch of a lima c c on bounding the fm phase breaks and forms two complex conjugate arcs we study the singularities and associated exponents of thermodynamic functions at the endpoints of these arcs for mu 0 there are two line segments of singularities on the negative and positive u axis and we carry out a similar study of the behavior at the inner endpoints of these arcs which constitute the nearest singularities to the origin in this case finally we also determine the exact complex temperature phase diagrams at mu 1 on the honeycomb and triangular lattices and discuss the relation between these and the corresponding zero field phase diagrams

yang lee edge singularity of a one dimensional ising ferromagnet with arbitrary spin it is shown that for a one dimensional lattice system in a purely imaginary magnetic field if the interaction is finite range the nature of the yang lee edge singularity is universal independent of the spin and interaction strengths the edge singularity corresponds to the twofold degeneracy of the largest eigenvalues of the transfer matrix for the blume emery griffiths ferromagnet the tricritical point and the edge pseudosingularity may exist the tricritical point corresponds to the triple degeneracy of the eigenvalues the edge pseudosingularity corresponds to the twofold degeneracy of the nonlargest eigenvalues

fisher zeros of the q state potts model in the complex temperature plane for nonzero external magnetic field the microcanonical transfer matrix is used to study the distribution of the fisher zeros of the qg2 potts models in the complex temperature plane with nonzero external magnetic field h q unlike the ising model for h q ensuremath ne 0 which has only a nonphysical critical point the fisher edge singularity the qg2 potts models have physical critical points for h q l0 as well as the fisher edge singularities for h q g0 for h q l0 the crossover of the fisher zeros of the q state potts model into those of the q ensuremath 1 state potts model is discussed and the critical line of the three state potts ferromagnet is determined for h q g0 we investigate the edge singularity for finite lattices and compare our results with the high field low temperature series expansion of enting for 3l ql 6 we find that the specific heat magnetization susceptibility and the density of zeros diverge at the fisher edge singularity with exponents ensuremath alpha e ensuremath beta e and ensuremath gamma e which satisfy the scaling law ensuremath alpha e 2 ensuremath beta e ensuremath gamma e 2

partition function zeros of the antiferromagnetic spin 1 2 ising heisenberg model on a diamond chain abstract the partition function zeros of the antiferromagnetic spin 1 2 ising heisenberg model on a diamond chain are studied using the transfer matrix method analytical equations for the distributions of yang lee and fisher zeros are derived the yang lee zeros are located on an arc of the unit circle and on the negative real axis in the complex magnetic fugacity plane in the limit t 0 the distribution pinches the positive real axis precipitating a phase transition fisher zeros manifest more complicated distributions depending on the values of the exchange parameters and external field densities of both categories of zeros are also studied the distributions of fisher zeros are investigated for different values of model parameters the yang lee and fisher edge singularity exponents are shown to be identical they are universal in nature and are calculated to be 1 2

generalized partition function zeros of 1d spin models and their critical behavior at edge singularities here we study the partition function zeros of the one dimensional blume emery griffiths model close to their edge singularities the model contains four couplings h j k including the magnetic field h and the ising coupling j we assume that only one of the three couplings j k is complex and the magnetic field is real the generalized zeros zi tend to form continuous curves on the complex z plane in the thermodynamic limit the linear density at the edges ze diverges usually with z z ze and 1 2 however as in the case of complex magnetic fields yang lee edge singularity if we have a triple degeneracy of the transfer matrix eigenvalues a new critical behavior with 2 3 can appear as we prove here explicitly for the cases where either or k is complex our proof applies for a general three state spin model with short range interactions the fisher zeros complex j are more involved in practice we have not been able to find an explicit example with 2 3 as far as the other couplings h k are kept as real numbers our results are supported by numerical computations of zeros we show that it is absolutely necessary to have a non vanishing magnetic field for a new critical behavior the appearance of 2 3 at the edge closest to the positive real axis indicates its possible relevance for tricritical phenomena in higher dimensional spin models

the yang lee zeros of the 1d blume capel model on connected and non connected rings we carry out a numerical and analytic analysis of the yang lee zeros of the 1d blume capel model with periodic boundary conditions and its generalization on feynman diagrams for which we include sums over all connected and non connected rings for a given number of spins in both cases for a specific range of the parameters the zeros originally on the unit circle are shown to depart from it as we increase the temperature beyond some limit the curve of zeros can bifurcate and become two disjoint arcs as in the 2d case we also show that in the thermodynamic limit the zeros of both blume capel models on the static connected ring and on the dynamical feynman diagrams lattice tend to overlap in the special case of the 1d ising model on feynman diagrams we can prove for arbitrary number of spins that the yang lee zeros must be on the unit circle the proof is based on a property of the zeros of legendre polynomials

the partition function zeros for a potts model of helix coil transition with three site interactions abstract the partition function fisher zeros of the q state potts model with three site interactions on a zigzag ladder are studied by a transfer matrix approach this q state model is proposed as a description of helix coil transition in homopolymers the fisher zeros are exactly derived for arbitrary value of the system parameter q it is shown that there is only a quasi phase transition for all temperatures the dependence of the helix coil transition on solvent is analyzed using fisher zeros of the model the densities of the fisher zeros are singular at the edge singularity points and the critical exponent 1 2

potts model on a cayley tree and logistic equation the q state potts model on a cayley tree can be solved by a recursion formula depending on the properties at the surface the model on a bethe lattice is obtained by extrapolating the interior of a cayley tree sufficiently far from the surface in order to have a stable fixed point of the recursion for q 2 we find a second order transition of percolation type at the bethe peierls temperature and a first order transition at a higher temperature for coordination number z 3 the recursion extrapolated to q 1 is identical to the logistic equation the feigenbaum route to chaos appears for antiferromagnetic coupling of the potts model the first period doubling corresponds to a multicritical point in the phase diagram of the potts model

ground state entropy of potts antiferromagnets bounds series and monte carlo measurements we report several results concerning w ensuremath lambda q mathrm exp s 0 k b the exponent of the ground state entropy of the potts antiferromagnet on a lattice ensuremath lambda first we improve our previous rigorous lower bound on w mathrm hc q for the honeycomb hc lattice and find that it is extremely accurate it agrees to the first 11 terms with the large q series for w mathrm hc q second we investigate the heteropolygonal archimedean 4 ensuremath cdot 8 2 lattice derive a rigorous lower bound on w 4 ensuremath cdot 8 2 q and calculate the large q series for this function to o y 12 where y 1 q ensuremath 1 remarkably these agree exactly to all 13 terms calculated we also report monte carlo measurements and find that these are very close to our lower bound and series third we study the effect of non nearest neighbor couplings focusing on the square lattice with next nearest neighbor bonds

exact potts model partition function on strips of the triangular lattice abstract in this paper we present exact calculations of the partition function z of the q state potts model and its generalization to real q for arbitrary temperature on n vertex strip graphs of width ly 2 and arbitrary length of the triangular lattice with free cyclic and mobius longitudinal boundary conditions these partition functions are equivalent to tutte whitney polynomials for these graphs the free energy is calculated exactly for the infinite length limit of the graphs and the thermodynamics is discussed considering the full generalization to arbitrary complex q and temperature we determine the singular locus b in the corresponding c 2 space arising as the accumulation set of partition function zeros as n in particular we study the connection with the t 0 limit of the potts antiferromagnet where b reduces to the accumulation set of chromatic zeros comparisons are made with our previous exact calculation of potts model partition functions for the corresponding strips of the square lattice our present calculations yield as special cases several quantities of graph theoretic interest

a unified pythagorean hodograph approach to the medial axis transform and offset approximation algorithms based on pythagorean hodographs ph in the euclidean plane and in minkowski space share common goals the main one being rationality of offsets of planar domains however only separate interpolation techniques based on these curves can be found in the literature it was recently revealed that rational ph curves in the euclidean plane and in minkowski space are very closely related in this paper we continue the discussion of the interplay between spatial mph curves and their associated planar ph curves from the point of view of hermite interpolation on the basis of this approach we design a new simple interpolation algorithm the main advantage of the unifying method presented lies in the fact that it uses after only some simple additional computations an arbitrary algorithm for interpolation using planar ph curves also for interpolation using spatial mph curves we present the functionality of our method for g 1 hermite data however one could also obtain higher order algorithms

upper and lower bounds for the ground state entropy of antiferromagnetic potts models we derive rigorous upper and lower bounds for the ground state entropy of the q state potts antiferromagnet on the honeycomb and triangular lattices these bounds are quite restrictive especially for large q copyright ital 1997 ital the american physical society

parallel replacement under capital rationing constraints contrary to serial replacement parallel replacement problems require a decision maker to evaluate a portfolio of replacement decisions in each time period because of economic interdependencies among assets in this paper we describe a parallel replacement problem in which the economic interdependence among assets is caused by capital rationing the research was motivated by the experience gained from a vehicle fleet replacement study where solutions to serial replacement problems could not be implemented since they violated management s budget plan when firms use budgets to control their expenditures competition for the limited funds creates interdependent problems in this paper we formulate the problem as a zero one integer program and develop a branch and bound algorithm based on lagrangian relaxation methodology a multiplier adjustment method is developed to solve one lagrangian dual

replica symmetry breaking in finite connectivity systems a large connectivity expansion at finite and zero temperature parisi replica symmetry breaking is extended to random bond systems with finite fixed connectivity m 1 the free energy f is explicitly calculated for large m within the first stage of symmetry breaking at finite temperature t the 1 m expansion is found to diverge as t to o indeed direct evaluation at zero temperature shows that the large m expansion is in powers of 1 m introduction of symmetry breaking brings the value of f close approximately 1 for 10 m 20 to numerical estimates of banavar et al the same techniques apply to systems with average finite connectivity

equivalence of ferromagnetic spin models on trees and random graphs recently we have found identical behaviour for various spin models on thin random graphs feynman diagrams and the corresponding bethe lattices in this paper we observe that the ratios of the saddle point equations in the random graph approach are identical to the fixed point s of the recursion relations which are used to solve the models on the bethe lattice the loops in the random graphs thus have no influence on the thermodynamic limit for such ferromagnetic spin models we consider the correspondence explicitly for ising and q state potts models and also note that multispin interaction models on cacti admit a similar correspondence with a randomized version of the cacti graphs which contain loops

yang lee zeros of the two and three state potts model defined on phi3 feynman diagrams we present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q 2 state ising and the q 3 state potts model defined on phi 3 feynman diagrams thin random graphs our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions for the case of the ising model an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the yang lee zeros are located on the unit circle although no circle theorem is known in this case of random graphs for the q 3 state potts model our perturbative results indicate that the yang lee zeros lie outside the unit circle both analytic results are confirmed by finite lattice numerical calculations

graph bipartitioning and statistical mechanics the problem of bipartitioning a random graph of fixed finite local valence connectivity so as to minimise the number of cross edges is studied by the application of monte carlo simulation of thermodynamics and annealing this problem is np complete and is relevant as an idealisation of several practical organisation problems evidence is presented for the existence of a multiplicity of metastable states and for non self averaging and ultrametricity in the space of overlaps albeit with a possible critical valence an empirical formula is presented for the optimal cost in excellent accord with values obtained by simulation and those known exactly

one dimensional potts model lee yang edges and chaos it is known that the exact renormalization transformations for the one dimensional ising model in a field can be cast in the form of the logistic map f x 4x 1 x with x a function of the ising couplings k and h the locus of the lee yang zeros for the one dimensional ising model in the k h plane is given by the julia set of the logistic map in this paper we show that the one dimensional q state potts model for q or 1 also displays such behavior a suitable combination of couplings which reduces to the ising case for q 2 can again be used to define an x satisfying f x 4x 1 x the lee yang zeros no longer lie on the unit circle in the complex z e h plane for q not equal 2 but their locus still maps onto the julia set of the logistic map

structural properties of potts model partition functions and chromatic polynomials for lattice strips abstract the q state potts model partition function equivalent to the tutte polynomial for a lattice strip of fixed width l y and arbitrary length l x has the form z g q v j 1 n z g c z g j z g j l x where v is a temperature dependent variable the special case of the zero temperature antiferromagnet v 1 is the chromatic polynomial p g q using coloring and transfer matrix methods we give general formulas for c x g j 1 n x g c x g j for x z p on cyclic and mobius strip graphs of the square and triangular lattice combining these with a general expression for the unique coefficient c z g j of degree d in q c d u 2d q 2 where u n x is the chebyshev polynomial of the second kind we determine the number of z g j s with coefficient c d in z g q v for these cyclic strips of width l y to be n z l y d 2d 1 l y d 1 1 2l y l y d for 0 d l y and zero otherwise for both cyclic and mobius strips of these lattices the total number of distinct eigenvalues z g j is calculated to be n z l y 2l y l y results are also presented for the analogous numbers n p l y d and n p l y for p g q we find that n p l y 0 n p l y 1 1 m l y 1 motzkin number n z l y 0 c l y the catalan number and give an exact expression for n p l y our results for n z l y and n p l y apply for both the cyclic and mobius strips of both the square and triangular lattices we also point out the interesting relations n z l y 2 n da tri l y and n p l y 2 n da sq l y where n da n denotes the number of directed lattice animals on the lattice we find the asymptotic growths n z l y l y 1 2 4 l y and n p l y l y 1 2 3 l y as l y some general geometric identities for potts model partition functions are also presented

a potts ising correspondence on thin graphs we note that it is possible to construct a bond vertex model that displays q state potts criticality on an ensemble of 3 random graphs of arbitrary topology which we denote as thin random graphs in contrast to the fat graphs of the planar diagram expansion since the four vertex model in question also serves to describe the critical behaviour of the ising model in field the formulation reveals an isomorphism between the potts and ising models on thin random graphs on planar graphs a similar correspondence is present only for q 1 the value associated with percolation