two and three spin triangular ising model variational approximations the implications of the known hard hexagon lattice gas results for the triangular ising model with both pair and triplet interactions are pointed out employing an appropriate generalization of the variational method of baxter we determine using the lowest order approximation the phase boundaries for this model when the pair interactions are ferromagnetic higher approximations are presented for the case of pure triplet interactions and the resulting phase diagrams are in excellent agreement with all exactly known results

on the application of the critical minimum energy subspace method to disordered systems abstract we discuss the recent application to strongly disordered systems of the critical minimum energy subspace crmes method used to limit the energy subspace of the wang landau sampling we compare with our results on the 3d random field ising model obtained by a multi range wang landau simulation over the whole energy range we point out some problems that may arise when applying the crmes scheme to models having a complex free energy landscape

universal features and tail analysis of the order parameter distribution of the two dimensional ising model an entropic sampling monte carlo study we present a numerical study of the order parameter probability density function pdf of the square ising model for lattices with linear sizes l 80 140 a recent efficient entropic sampling scheme combining the wang landau and broad histogram methods and based on the high levels of the wang landau process in dominant energy subspaces is employed we find that for large lattices there exists a stable window of the scaled order parameter in which the full ansatz including the pre exponential factor for the tail regime of the universal pdf is well obeyed this window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal pdf the probability densities are used to estimate the universal privman fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime

the random field ising model with an asymmetric trimodal probability distribution the ising model in the presence of a random field is investigated within the mean field approximation based on landau expansion the random field is drawn from the trimodal probability distribution p hi p hi h0 q hi h0 r hi where the probabilities p q r take on values within the interval 0 1 consistent with the constraint p q r 1 asymmetric distribution hi is the random field variable and h0 the respective strength this probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites the current random field ising system displays second order phase transitions which for some values of p q and h0 are followed by first order phase transitions thus confirming the existence of a tricritical point and in some cases two tricritical points also reentrance can be seen for appropriate ranges of the aforementioned variables using the variational principle we determine the equilibrium equation for magnetization solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h0

monte carlo analysis of the critical properties of the two dimensional randomly bond diluted ising model via wang landau algorithm abstract the influence of random bond dilution on the critical properties of the two dimensional ising model on a square lattice with periodic boundary conditions is presented using the monte carlo process with wang landau sampling the lattice linear size is l 20 140 and the concentration of the diluted bonds spans a wide range from weak to strong dilution namely q 0 05 0 1 0 2 0 3 0 4 the respective percolation limit for the square lattice is q c p e r c 0 5 its pure version q 0 has a second order phase transition with vanishing specific heat critical exponent an example of inapplicability of the harris criterion the main effort is focused on the temperature dependence of the specific heat and magnetic susceptibility to estimate the respective maximum values and subsequent pseudocritical temperatures for extracting the relative critical exponents we have also looked at the probability distribution of the susceptibility pseudocritical temperature and specific heat for assessing self averaging the study is carried out in the appropriately restricted but dominant energy subspaces by applying the finite size scaling analysis the critical exponents are estimated the specific heat exponent vanishes the correlation length exponent is equal to one and the critical exponents ratio retains its pure ising model value thus supporting the strong universality hypothesis

relaxation of an optimal control problem involving a perturbed sweeping process we establish first in the setting of infinite dimensional hilbert space a result concerning the existence of solutions for perturbed sweeping processes whose perturbations are lipschitz single valued maps then we use this result to extend to the infinite dimensional setting a relaxation result concerning optimal control problems involving such processes

determining the density of states for classical statistical models a random walk algorithm to produce a flat histogram we describe an efficient monte carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models the density of states is modified at each step when the energy level is visited to produce a flat histogram by carefully controlling the modification factor we allow the density of states to converge to the true value very quickly even for large systems from the density of states at the end of the random walk we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature using this method we not only can avoid repeating simulations at multiple temperatures but we can also estimate the free energy and entropy quantities that are not directly accessible by conventional monte carlo simulations this algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability as with the multicanonical monte carlo technique our method overcomes the tunneling barrier between coexisting phases at first order phase transitions in this paper we apply our algorithm to both first and second order phase transitions to demonstrate its efficiency and accuracy we obtained direct simulational estimates for the density of states for two dimensional ten state potts models on lattices up to 200 x 200 and ising models on lattices up to 256 x 256 our simulational results are compared to both exact solutions and existing numerical data obtained using other methods applying this approach to a three dimensional j spin glass model we estimate the internal energy and entropy at zero temperature and using a two dimensional random walk in energy and order parameter space we obtain the rough canonical distribution and energy landscape in order parameter space preliminary data suggest that the glass transition temperature is about 1 2 and that better estimates can be obtained with more extensive application of the method this simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space

optimizing network attacks by artificial bee colony abstract over the past few years the task of conceiving effective attacks to complex networks has arisen as an optimization problem attacks are modelled as the process of removing a number k of vertices from the graph that represents the network and the goal is to maximise or minimise the value of a predefined metric over the graph in this work we present an optimization problem that concerns the selection of nodes to be removed to minimise the maximum betweenness centrality value of the residual graph this metric evaluates the participation of the nodes in the communications through the shortest paths of the network to address the problem we propose an artificial bee colony algorithm which is a swarm intelligence approach inspired in the foraging behaviour of honeybees in this framework bees produce new candidate solutions for the problem by exploring the vicinity of previous ones called food sources the proposed method exploits useful problem knowledge in this neighbourhood exploration by considering the partial destruction and heuristic reconstruction of selected solutions the performance of the method with respect to other models from the literature that can be adapted to face this problem such as sequential centrality based attacks module based attacks a genetic algorithm a simulated annealing approach and a variable neighbourhood search is empirically shown

identification and prediction of dynamic systems using an interactively recurrent self evolving fuzzy neural network this paper presents a novel recurrent fuzzy neural network called an interactively recurrent self evolving fuzzy neural network irsfnn for prediction and identification of dynamic systems the recurrent structure in an irsfnn is formed as an external loops and internal feedback by feeding the rule firing strength of each rule to others rules and itself the consequent part in the irsfnn is composed of a takagi sugeno kang tsk or functional link based type the proposed irsfnn employs a functional link neural network flnn to the consequent part of fuzzy rules for promoting the mapping ability unlike a tsk type fuzzy neural network the flnn in the consequent part is a nonlinear function of input variables an irsfnns learning starts with an empty rule base and all of the rules are generated and learned online through a simultaneous structure and parameter learning an on line clustering algorithm is effective in generating fuzzy rules the consequent update parameters are derived by a variable dimensional kalman filter algorithm the premise and recurrent parameters are learned through a gradient descent algorithm we test the irsfnn for the prediction and identification of dynamic plants and compare it to other well known recurrent fnns the proposed model obtains enhanced performance results

continuous phase transitions with a convex dip in the microcanonical entropy the appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition however a convex dip also shows up in some systems with a continuous transition as for example in the baxter wu model and in the four state potts model in two dimensions we demonstrate that the appearance of a convex dip in those cases can be traced back to a finite size effect the properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite size scaling theory for continuous phase transitions results obtained from numerical simulations corroborate the predictions of the scaling theory

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

phase behavior under the averaging over disorder realizations abstract effects of the averaging over disorder realizations samples on the phase behavior are analyzed in terms of the mean field approximation for the random field ising model with infinite range interactions it is found that the averaging is equivalent to a drastic modification in the statistics of the quenched variables in its turn this lowers the critical temperature of a second order phase transition or depending on the sampling even suppresses the ordered phase possible first order transitions are shown to be softened by the sample averaging common issues and differences in the interpretation of these effects in the context of the simulation and experimental studies are discussed

lack of self averaging of the specific heat in the three dimensional random field ising model we apply the recently developed critical minimum energy subspace scheme for the investigation of the random field ising model we point out that this method is well suited for the study of this model the density of states is obtained via the wang landau and broad histogram methods in a unified implementation by employing the n fold version of the wang landau scheme the random fields are obtained from a bimodal distribution h i ifmmode pm else textpm fi 2 and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from l 4 to l 32 observing the finite size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat the lack of self averaging of this quantity is fully illustrated and it is shown that this property may be related to the question mentioned above

finite size scaling analysis of the critical behavior of the baxter wu model abstract we use the recently developed critical minimum energy subspace crmes approximation scheme to study the critical behavior of the baxter wu model this scheme uses only a properly determined part of the energy spectrum and allows us to obtain high accuracy for relatively large systems with considerably reduced computational effort the density of states is constructed by a multi range wang landau sampling and from this we obtain the critical properties of specific heat and of the reduced binder cummulant the good agreement of our results with existing exact solutions demonstrates the accuracy of our approximation technique

the random field ising model with an asymmetric and anisotropic bimodal probability distribution abstract the ising model in the presence of a random field drawn from the asymmetric and anisotropic trimodal probability distribution p h i p h i h 0 q h i h 0 r h i is investigated the partial probabilities p q r take on values within the interval 0 1 consistent with the constraint p q r 1 asymmetric distribution h i is the random field variable with basic absolute value h 0 strength is the competition parameter which is the ratio between the respective strength of the random magnetic field in the two principal directions z and z and is positive so that the random fields are competing anisotropic distribution this probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites the current random field ising system displays mainly second order phase transitions which for some values of p q and h 0 are followed by first order phase transitions joined smoothly by a tricritical point occasionally two tricritical points appear implying another second order phase transition in addition to these points re entrant phenomena can be seen for appropriate ranges of the temperature and random field for specific values of p and q using the variational principle we write down the equilibrium equation for the magnetization and solve it for both phase transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0 considered as an independent variable in addition to the temperature

the sherrington kirkpatrick spin glass model in the presence of a random field with a joint gaussian probability density function for the exchange interactions and random fields abstract the magnetic systems with disorder form an important class of systems which are under intensive studies since they reflect real systems such a class of systems is the spin glass one which combines randomness and frustration the sherrington kirkpatrick ising spin glass with random couplings in the presence of a random magnetic field is investigated in detail within the framework of the replica method the two random variables exchange integral interaction and random magnetic field are drawn from a joint gaussian probability density function characterized by a correlation coefficient the thermodynamic properties and phase diagrams are studied with respect to the natural parameters of both random components of the system contained in the probability density the de almeida thouless line is explored as a function of temperature and other system parameters the entropy for zero temperature as well as for non zero temperatures is partly negative or positive acquiring positive branches as h 0 increases

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

a hybrid particle swarm optimizer with sine cosine acceleration coefficients abstract particle swarm optimization pso has been widely used to solve complex global optimization tasks due to its implementation simplicity and inexpensive computational overhead however pso has premature convergence is easily trapped in the local optimum solution and is ineffective in balancing exploration and exploitation especially in complex multi peak search functions to overcome the shortcomings of pso a hybrid particle swarm optimizer with sine cosine acceleration coefficients h pso scac is proposed to solve these problems it is verified by the application of twelve numerical optimization problems in h pso scac we make the following improvements first we introduce sine cosine acceleration coefficients scac to efficiently control the local search and convergence to the global optimum solution second opposition based learning obl is adopted to initialize the population additionally we utilize a sine map to adjust the inertia weight finally we propose a modified position update formula experimental results show that in the majority of cases the h pso scac approach is capable of efficiently solving numerical optimization tasks and outperforms the existing similar population based algorithms and pso variants proposed in recent years therefore the h pso scac algorithm is successfully employed as a novel optimization strategy

estimation of critical behavior from the density of states in classical statistical models we present a simple and efficient approximation scheme which greatly facilitates the extension of wang landau sampling or similar techniques in large systems for the estimation of critical behavior the method presented in an algorithmic approach is based on a very simple idea familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem it is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters it is proposed that the extensions of the finite size critical part of the energy space determining the specific heat satisfy a scaling law involving the thermal critical exponent the method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic ising lattices the proposed scaling law is verified by estimating the thermal critical exponent from the finite size behavior of the critical part of the energy space the density of states of the zero field ising model on these lattices is obtained via a multirange wang landau sampling

wang landau study of the critical behavior of the bimodal 3d random field ising model we apply the wang landau method to the study of the critical behavior of the three dimensional random field ising model with a bimodal probability distribution for high values of the random field intensity we find that the energy probability distribution at the transition temperature is double peaked suggesting that the phase transition is first order on the other hand the transition looks continuous for low values of the field intensity in spite of the large sample to sample fluctuations observed the double peak in the probability distribution is always present for high fields

baxter wu model in the presence of an external magnetic field abstract in this work we study an unusual phase transition of the baxter wu model in the presence of an external magnetic field the model is pure baxter wu which means that only three spin interactions are taken into account we construct a phase diagram on the temperature field plane based mainly on the singularities of the specific heat these singularities are more clearly observed than those of the magnetic susceptibility which are used in existing works we establish a discontinuity in the critical exponents when the field is changed from zero to negative

entropic sampling via wang landau random walks in dominant energy subspaces dominant energy subspaces of statistical systems are defined with the help of restrictive conditions on various characteristics of the energy distribution such as the probability density and the fourth order binder s cumulant our analysis generalizes the ideas of the critical minimum energy subspace crmes technique applied previously to study the specific heat s finite size scaling here we illustrate alternatives that are useful for the analysis of further finite size anomalies and the behavior of the corresponding dominant subspaces is presented for the two dimensional 2d baxter wu and the 2d and 3d ising models in order to show that a crmes technique is adequate for the study of magnetic anomalies we study and test simple methods which provide the means for an accurate determination of the energy order parameter e m histograms via wang landau random walks the 2d ising model is used as a test case and it is shown that high level wang landau sampling schemes yield excellent estimates for all magnetic properties our estimates compare very well with those of the traditional metropolis method the relevant dominant energy subspaces and dominant magnetization subspaces scale as expected with exponents alpha nu and gamma nu respectively using the metropolis method we examine the time evolution of the corresponding dominant magnetization subspaces and we uncover the reasons behind the inadequacy of the metropolis method to produce a reliable estimation scheme for the tail regime of the order parameter distribution

critical endpoint behavior in an asymmetric ising model application of wang landau sampling to calculate the density of states using the wang landau sampling method with a two dimensional random walk we determine the density of states for an asymmetric ising model with two and three body interactions on a triangular lattice in the presence of an external field with an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite size analyses at and away from the critical endpoint we observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint and the exponents for both divergences agree well with previous theoretical predictions

lack of self averaging in random systems liability or asset abstract the study of quenched random systems is facilitated by the idea that the ensemble averages describe the thermal averages for any specific realization of the couplings provided that the system is large enough careful examination suggests that this idea might have a flaw when the correlation length becomes of the order of the size of the system we find that certain bounded quantities are not self averaging when the correlation length becomes of the order of the size of the system this suggests that the lack of self averaging expressed in terms of properly chosen signal to noise ratios may serve to identify phase boundaries this is demonstrated by using such signal to noise ratios to identify the boundary of the ferromagnetic phase of the random field ising system and compare the findings with more traditional measures

bv solutions of nonconvex sweeping process differential inclusion with perturbation abstract this paper is devoted to the study of differential inclusions particularly discontinuous perturbed sweeping processes in the infinite dimensional setting on the one hand the sets involved are assumed to be prox regular and to have a variation given by a function which is of bounded variation and right continuous on the other hand the perturbation satisfies a linear growth condition with respect to a fixed compact subset finally the case where the sets move in an absolutely continuous way is recovered as a consequence

scaling properties of the baxter wu model abstract we use a recently developed cluster algorithm for the baxter wu model to study characteristic features of its behavior magnetic scaling properties of the model are investigated for second order phase transitions we improve significantly the accuracy of monte carlo simulation results and we provide new results for the behavior of the binder cumulants for temperatures below above and at the critical point

projection process with definable right hand side we study the relation between sweeping processes with the cone of limiting normals and projection processes we prove the existence of a solution of a perturbed sweeping process with the cone of limiting normals and of nonstationary projection processes provided the sets involved are definable and are moving in a definable way in some o minimal structure an application to a crowd motion model is presented

critical energy distribution function of the baxter wu model abstract in this work we examine the critical finite size scaling behavior of the energy probability distribution function and its corresponding binder cumulant at critical point based on the results of monte carlo simulations at zero external magnetic field using the recently developed triangle cluster algorithm we calculate the energy distribution function s exponents and we derive the scaling relations for the energy binder cumulant finally we predict the exact form of the scaled energy distribution function most of our conclusions seem applicable not only to the baxter wu model but also to other ising like models

first order transition features of the triangular ising model with nearest and next nearest neighbor antiferromagnetic interactions abstract we implement a new and accurate numerical entropic scheme to investigate the first order transition features of the triangular ising model with nearest neighbor j nn and next nearest neighbor j nnn antiferromagnetic interactions in ratio r j nn j nnn 1 important aspects of the existing theories of first order transitions are briefly reviewed tested on this model and compared with previous work on the potts model using lattices with linear sizes l 30 40 100 120 140 160 200 240 360 and 480 we estimate the thermal characteristics of the present weak first order transition our results improve the original estimates of rastelli et al and verify all the generally accepted predictions of the finite size scaling theory of first order transitions including transition point shifts thermal and magnetic anomalies however two of our findings are not compatible with current phenomenological expectations the behavior of transition points derived from the number of phases parameter is not in accordance with the theoretically conjectured exponentially small shift behavior and the well known double gaussian approximation does not correctly describe higher correction terms of the energy cumulants it is argued that this discrepancy has its origin in the commonly neglected contributions from domain wall corrections

a novel approach to statistical comparison of meta heuristic stochastic optimization algorithms using deep statistics abstract in this paper a novel approach for making a statistical comparison of meta heuristic stochastic optimization algorithms over multiple single objective problems is introduced where a new ranking scheme is proposed to obtain data for multiple problems the main contribution of this approach is that the ranking scheme is based on the whole distribution instead of using only one statistic to describe the distribution such as average or median averages are sensitive to outliers i e the poor runs of the stochastic optimization algorithms and consequently medians are sometimes used however using the common approach with either averages or medians the results can be affected by the ranking scheme that is used by some standard statistical tests this happens when the differences between the averages or medians are in some neighborhood and the algorithms obtain different ranks though they should be ranked equally given the small differences that exist between them the experimental results obtained on black box benchmarking 2015 show that our approach gives more robust results compared to the common approach in cases when the results are affected by outliers or by a misleading ranking scheme

the random field ising model with asymmetric bimodal probability distribution abstract the ising model in the presence of a random field is investigated within the mean field approximation based on landau expansion the random field is drawn from the bimodal probability distribution p h p h h 0 1 p h h 0 where the probability p assumes any value within the interval 0 1 asymmetric distribution the prevailing transitions are of second order but for some values of p and h 0 first order phase transitions take place for smaller temperatures and higher h 0 thus confirming the existence of a tricritical point also the possible reentrant phenomena in the phase diagram t h 0 plane occur for appropriate values of p and h 0 using the variational principle we determine the equilibrium equation for magnetization and solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0

self averaging in many body quantum systems out of equilibrium time dependence of distributions in a disordered system a quantity is self averaging when the ratio between its variance for disorder realizations and the square of its mean decreases as the system size increases here we consider a chaotic disordered many body quantum system and search for a relationship between self averaging behavior and the properties of the distributions over disorder realizations of various quantities and at different timescales an exponential distribution as found for the survival probability at long times explains its lack of self averaging since the mean and the dispersion are equal gaussian distributions however are obtained for both self averaging and non self averaging quantities our studies show also that one can make conclusions about the self averaging behavior of one quantity based on the distribution of another related quantity this strategy allows for semianalytical results and thus circumvents the limitations of numerical scaling analysis which are restricted to few system sizes

finite size scaling at first and second order phase transitions of baxter wu model abstract using a finite size phenomenological theory we investigate the behavior of the baxter wu model for both first and second order transitions in order to distinguish between the two kinds of transition we study the finite size scaling behavior of the order parameter and the susceptibility of the model at the critical temperature the known critical exponents of the system govern the scaling behavior while below the critical temperature the scaling exponents are the dimensionality of the system the presented scaling theory for the baxter wu model is an appropriate generalization of the corresponding theory of binder and landau for the ising model binder and landau phys rev b 30 1984 1477 we perform numerical simulations using standard monte carlo techniques and we find that our results are in good agreement with theoretical predictions

sweeping process with regular and nonregular sets abstract differential inclusions involving the normal cone to a moving set are investigated a special attention is paid to the sweeping process associated with sets for which no regularity assumption is required

conformal invariance studies of the baxter wu model and a related site colouring problem the partition function of the baxter wu model is exactly related to the generating function of a site colouring problem on a hexagonal lattice we extend the original bethe ansatz solution of these models in order to obtain the eigenspectra of their transfer matrices in finite geometries and general toroidal boundary conditions the operator content of these models is studied by solving numerically the bethe ansatz equations and by exploring conformal invariance since the eigenspectra are calculated for large lattices the corrections to finite size scaling are also calculated