a two unit general parallel system with n 2 cold standbys analytic and simulation approach abstract a parallel 2 n 2 system is investigated here where two units start their operation simultaneously and any one of them is replaced instantaneously upon its failure by one of the n 2 cold standbys we assume availability of n non identical non repairable units for replacement or support the system reliability is evaluated by recursive relations with unit lifetimes t i i 1 n that have a general joint distribution function f t on the basis of the derived expression simulation techniques have been developed for the evaluation of the system reliability and the mean time to failure useful when dealing with large systems or correlated unit lifetimes and less mathematically manageable distributions simulation results are presented for various lifetime distributions and comparisons are made with derived analytic results for some special distributions and moderate values of n

crossover and self averaging in the two dimensional site diluted ising model application of probability changing cluster algorithm using the newly proposed probability changing cluster pcc monte carlo algorithm we simulate the two dimensional 2d site diluted ising model since we can tune the critical point of each random sample automatically with the pcc algorithm we succeed in studying the sample dependent t c l and the sample average of physical quantities at each t c l systematically using the finite size scaling fss analysis for t c l we discuss the importance of corrections to fss both in the strong dilution and weak dilution regions the critical phenomena of the 2d site diluted ising model are shown to be controlled by the pure fixed point the crossover from the percolation fixed point to the pure ising fixed point with the system size is explicitly demonstrated by the study of the binder parameter we also study the distribution of critical temperature t c l its variance shows the power law l dependence l ensuremath n and the estimate of the exponent n is consistent with the prediction of aharony and harris phys rev lett 77 3700 1996 calculating the relative variance of critical magnetization at the sample dependent t c l we show that the 2d site diluted ising model exhibits weak self averaging

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

universal finite size scaling functions with exact nonuniversal metric factors using exact partition functions and finite size corrections for the ising model on finite square plane triangular and honeycomb lattices and extending a method j phys 19 l1215 1986 to subtract leading singular terms from the free energy we obtain universal finite size scaling functions for the specific heat internal energy and free energy of the ising model on these lattices with exact nonuniversal metric factors

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

universality class of the two dimensional site diluted ising model in this work we evaluate the probability distribution function of the order parameter for the two dimensional site diluted ising model extensive monte carlo simulations have been performed for different spin concentrations p 0 70 ensuremath le p ensuremath le 1 on square lattices with linear sizes l 20 ensuremath le l ensuremath le 100 the results indicate that the universality class of the diluted ising model seems to be independent of the amount of dilution logarithmic corrections of the finite size critical temperature behavior of the model can also be inferred even for such small lattices

logarithmic corrections to correlation decay in two dimensional random bond ising systems the statistics of critical spin spin correlation functions in ising systems with nonfrustrated disorder are investigated on a strip geometry via numerical transfer matrix techniques conformal invariance concepts are used in order to test for logarithmic corrections to pure power law decay against distance fits of our data to conformal invariance expressions specific to logarithmic corrections to correlations on strips give results with the correct sign for the moments of order n 0 ensuremath 4 of the correlation function distribution we find an interval of disorder strength along which corrections to pure system behavior can be decomposed into the product of a known n dependent factor and an approximately n independent one in accordance with predictions a phenomenological fitting procedure is proposed which takes partial account of subdominant terms of correlation function decay on strips in the low disorder limit it gives results in fairly good agreement with theoretical predictions provided that an additional assumption is made

softening of first order transition in three dimensions by quenched disorder we study by extensive monte carlo simulations the effect of random bond dilution on the phase transition of the three dimensional four state potts model that is known to exhibit a strong first order transition in the pure case the phase diagram in the dilution temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes in the strongly disordered regime numerical evidence for softening to a second order transition induced by randomness is given here a large scale finite size scaling analysis made difficult due to strong crossover effects presumably caused by the percolation fixed point is performed

high temperature series analysis of the free energy and susceptibility of the 2d random bond ising model abstract we derive high temperature series expansions for the free energy and susceptibility of the two dimensional random bond ising model with a symmetric bimodal distribution of two positive coupling strengths j1 and j2 and study the influence of the quenched random bond disorder on the critical behavior of the model by analysing the series expansions over a wide range of coupling ratios j2 j1 covering the crossover from weak to strong disorder we obtain for the susceptibility with two different methods compelling evidence for a singularity of the form t 7 4 ln t 7 8 as predicted theoretically by shalaev shankar and ludwig for the specific heat our results are less convincing but still compatible with the theoretically predicted log log singularity

critical behavior of the pure and random bond two dimensional triangular ising ferromagnet we investigate the effects of quenched bond randomness on the critical properties of the two dimensional ferromagnetic ising model embedded in a triangular lattice the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method in the first part of our study we present the finite size scaling behavior of the pure model for which we calculate the critical amplitude of the specific heat s logarithmic expansion for the disordered system the numerical data and the relevant detailed finite size scaling analysis along the lines of the two well known scenarios logarithmic corrections versus weak universality strongly support the field theoretically predicted scenario of logarithmic corrections a particular interest is paid to the sample to sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality

universal dependence on disorder of two dimensional randomly diluted and random bond j ising models we consider the two dimensional randomly site diluted ising model and the random bond j ising model also called the edwards anderson model and study their critical behavior at the paramagnetic ferromagnetic transition the critical behavior of thermodynamic quantities can be derived from a set of renormalization group equations in which disorder is a marginally irrelevant perturbation at the two dimensional ising fixed point we discuss their solutions focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder then we present a finite size scaling analysis of high statistics monte carlo simulations the numerical results confirm the renormalization group predictions and in particular the universality of the logarithmic corrections to the ising behavior due to quenched dilution

critical exponents of the dilute ising model from four loop expansions four loop expansions of the coefficients of the callan symanzik equation for 3d and 2d dilute ising models are calculated fixed point coordinates and critical exponents are estimated by two methods of summation of double series a generalisation of the pade borel approximation and the first confluent form of the e algorithm of wynn summation of the double series for the 2d dilute ising model gives exponents very close to exponents of the pure ising model in accordance with the exact solution

scaling relations for logarithmic corrections multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical mechanical systems here a lee yang zero approach is used to systematically analyze the exponents of such logarithms and to propose scaling relations between them these proposed relations are then confronted with a variety of results from the literature

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

self consistent scaling theory for logarithmic correction exponents multiplicative logarithmic corrections frequently characterize critical behavior in statistical physics here a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific heat critical exponent vanishes also the theory is widened to encompass the correlation function the new relations are then confronted with results from the literature and some new predictions for logarithmic corrections in certain models are made

effect of random impurities on fluctuation driven first order transitions we analyse the effect of quenched uncorrelated randomness coupling to the local energy density of a model consisting of n coupled two dimensional ising models for n 2 the pure model exhibits a fluctuation driven first order transition characterized by runaway renormalization group behaviour we show that the addition of weak randomness acts to stabilize these flows in such a way that the trajectories ultimately flow back towards the pure decoupled ising fixed point with the usual critical exponents apart from logarithmic corrections we also show by examples that in higher dimensions such transitions may either become continuous or remain first order in the presence of randomness

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

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

critical behavior induced by quenched disorder abstract domain arguments and renormalization group calculations indicate that all temperature driven symmetry breaking first order phase transitions are converted to second order by quenched bond randomness this occurs for infinitesimal randomness in d 2 or d 4 respectively for discrete or continuous n 1 or n 2 component microscopic degrees of freedom even strongly first order transitions undergo this conversion to second order above these dimensions this conversion still occurs but requires a threshold bond randomness presumably with an intervening new tricritical point for example q state potts transitions can be made second order for any q in any d via bond randomness non symmetry breaking temperature driven first order transitions are eliminated under the above conditions these quenched fluctuation induced second order phase transitions suggest the possibility of new universality classes of criticality and tricriticality

exact finite size scaling corrections to the critical two dimensional ising model on a torus we analyse the finite size corrections to the energy and specific heat of the critical two dimensional spin ising model on a torus we extend the analysis of ferdinand and fisher to compute the correction of order l 3 to the energy and the corrections of order l 2 and l 3 to the specific heat we also obtain general results on the form of the finite size corrections to these quantities only integer powers of l 1 occur unmodified by logarithms except of course for the leading log l term in the specific heat and the energy expansion contains only odd powers of l 1 in the specific heat expansion any power of l 1 can appear but the coefficients of the odd powers are proportional to the corresponding coefficients of the energy expansion

critical behavior of the two dimensional spin diluted ising model via the equilibrium ensemble approach the equilibrium ensemble approach to disordered systems is used to investigate the critical behavior of the two dimensional ising model in the presence of quenched random site dilution the numerical transfer matrix technique in semi infinite strips of finite width together with phenomenological renormalization and conformal invariance is particularly suited to putting the equilibrium ensemble approach to work a method by which to extract with great precision the critical temperature of the model is proposed and applied a more systematic finite size scaling analysis than in previous numerical studies has been performed a parallel investigation along the lines of the two main scenarios currently under discussion namely the logarithmic corrections scenario with critical exponents fixed in the ising universality class versus the weak universality scenario critical exponents varying with the degree of disorder is carried out in interpreting our data maximum care is constantly taken to be open to both possibilities a critical discussion shows that an unambiguous discrimination between the two scenarios is still not possible on the basis of the available finite size data s1063 651x 99 16110 5

scaling analysis of the site diluted ising model in two dimensions a combination of recent numerical and theoretical advances are applied to analyze the scaling behavior of the site diluted ising model in two dimensions paying special attention to the implications for multiplicative logarithmic corrections the analysis focuses primarily on the odd sector of the model i e that associated with magnetic exponents and in particular on its lee yang zeros which are determined to high accuracy scaling relations are used to connect to the even thermal sector and a first analysis of the density of zeros yields information on the specific heat and its corrections the analysis is fully supportive of the strong scaling hypothesis and of the scaling relations for logarithmic corrections