@article{Uzelac2002, title = {The critical behaviour of the long-range Potts chain from the largest cluster probability distribution}, author = {Katarina Uzelac and Zvonko Glumac}, day = {01}, journal = {Physica A: Statistical Mechanics and its Applications}, month = {Nov}, number = {1-4}, pages = {448--453}, url = {http://www.sciencedirect.com/science/article/B6TVG-46871HY-S/1/eed89c6bf68a55aa24282a17cefd0c05}, volume = {314}, year = {2002}, biburl = {http://www.bibsonomy.org/bibtex/2f595e347350d19c2b3b2e8df48547989/smicha}, description = {Physica A}, keywords = {Phase transitions } } @article{Glumac1999, title = {Determination of the order of phase transitions in Potts model by the graph-weight approach}, author = {Zvonko Glumac and Katarina Uzelac}, day = {01}, journal = {Physica A: Statistical Mechanics and its Applications}, month = {Sep}, number = {1-2}, pages = {147--156}, url = {http://www.sciencedirect.com/science/article/B6TVG-3X9JGNV-D/1/52f848f3a82d1f20eb45d49f6fb4b110}, volume = {271}, year = {1999}, biburl = {http://www.bibsonomy.org/bibtex/26560930a7f89cf8302d32a2b8738ba46/smicha}, description = {Physica A}, keywords = {First-order transitions } } @article{Glumac2002, title = {Complex-q zeros of the partition function of the Potts model with long-range interactions}, author = {Zvonko Glumac and Katarina Uzelac}, day = {01}, journal = {Physica A: Statistical Mechanics and its Applications}, month = {Jul}, number = {1-2}, pages = {91--108}, url = {http://www.sciencedirect.com/science/article/B6TVG-45MWP57-7/1/bc27d364b84271a331ef1e440da73bea}, volume = {310}, year = {2002}, biburl = {http://www.bibsonomy.org/bibtex/26f9215f6de78605d753d48cd87122b69/smicha}, description = {Physica A}, keywords = {Phase transitions } } @article{journals/ijcm/TeofanovU07, title = {Family of quadratic spline difference schemes for a convection-diffusion problem.}, author = {Ljiljana Teofanov and Zorica Uzelac}, journal = {Int. J. Comput. Math.}, number = {1}, pages = {33-50}, url = {http://dblp.uni-trier.de/db/journals/ijcm/ijcm84.html#TeofanovU07}, volume = {84}, year = {2007}, biburl = {http://www.bibsonomy.org/bibtex/2b8f2b0c896e24763c49f330bb0bbc62f/dblp}, description = {dblp}, ee = {http://dx.doi.org/10.1080/00207160601138830}, date = {2008-02-03}, keywords = {dblp } } @incollection{statphys23_0874, title = {Short-time dynamics of the long-range Potts model}, address = {Genova, Italy}, author = {K. Uzelac and Z. Glumac}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=874}, year = {2007}, biburl = {http://www.bibsonomy.org/bibtex/2c218dab0445e05520921e6e841e6ae07/statphys23}, abstract = {The short-time dynamics [1] has recently attracted considerable attention by providing a ground for numerical calculation of static critical properties, which is free of critical slowing down. The concept may be extended to the long-range interactions, as it was shown for continuous n-vector and spherical models within the RG $\epsilon$-expansion [2]. We examine the applicability of dynamical Monte Carlo simulations based on this approach to discrete models with long-range interactions. We consider the one dimensional q-state Potts model with long-range power-law decaying interactions of the form $1/r^{1+\sigma}$. This paradigmatic model comprises, through variation of the parameter of range $\sigma$, different critical regimes, including the onset of the first-order phase transition when $q>2$. By using different dynamical procedures, we derive the static critical exponents, and study the universal dynamical critical exponent of the initial slip, depending on $\sigma$ and number of states $q$. Particular attention is given to the tricritical point, related to the onset of the first-order regime $q_c(\sigma)$, precise location of which still escapes to all the standard RG and numerical approaches [3]. \\ 1) H.K. Janssen, B. Schaub, and B. Schmittman, Z.Phys. B73, 539 (1989)\\ 2) Y. Chen et al, Eur.Phys.J. B 18, 289 (2000)\\ 3) E. Bayong et al., Phys.Rev.Lett. 83, 14 (1999); K. Uzelac, Z. Glumac, Phys.Rev.Lett. 85, 5255 (2000); S. Reynal, H.-T. Diep, Phys.Rev. E 69, 026109 (2004)}, keywords = {dynamics interactions long-range model potts short-time statphys23 topic-2 } } @incollection{statphys23_0809, title = {Short-time dynamics of the 1D three-state long-range Potts model}, address = {Genova, Italy}, author = {Z. Glumac and K. Uzelac}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=809}, year = {2007}, biburl = {http://www.bibsonomy.org/bibtex/2c5aedd7b29ed249e9abba5f57c22eb71/statphys23}, abstract = {We investigate the short-time dynamics of the one-dimensional $q = 3$ Potts model with a power-law decaying interactions of the form $r^{-(1 + \sigma)}$. This model is known to exhibit both first- and second-order transition regimes, which depend on the parameter of range $\sigma$ and are separated by a $q$-dependent tricritical point $\sigma_c(q)$ [1]. The location of this point, where the first-order transition becomes extremely weak presents difficulties both for RG approaches and for equilibrium numerical simulations [2-3]. We examine the first-order transition regime and its onset at $\sigma_c$ by dynamic Monte Carlo simulations, which recently appeared to be efficient in detecting weak first-order phase transitions [4]. We consider the short-time relaxation processes for magnetization and its higher momenta starting from high and low temperatures. We analyse the appearance of two pseudo critical temperatures characteristic for the first-order transition regime, which should merge at the tricritical point. \\ 1) Z. Glumac and K. Uzelac, Phys. Rev. E 58, 4372 (1998) \\ 2) E. Bayong, H. T. Diep, V. Dotsenko, Phys. Rev. Lett. 83, 14 (1999); K. Uzelac and Z. Glumac, Phys. Rev. Lett. 85, 5255 (2000) \\ 3) Sylvain Reynal, Hung-The Diep, Phys. Rev. E 69, 026109 (2004)\\ 4) L. Schuelke nad B. Zhang, Phys. Rev. E 62, 7482 (2000)}, keywords = {dynamics first-order interactions long-range model potts short-time statphys23 threshold topic-2 transition } } @incollection{statphys23_0788, title = {Phase transitions in the totally asymmetric exclusion process with long-range hopping}, address = {Genova, Italy}, author = {J. Szavits Nossan and K. Uzelac}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=788}, year = {2007}, biburl = {http://www.bibsonomy.org/bibtex/2f055ce996344f8653e855db40e6db0d2/statphys23}, abstract = {Importance of the effective long-range interactions [1] appearing in asymmetric exclusion processes (ASEP) raises the questions of possible consequences that an explicit introduction of long-range effects might have on the boundary-induced phase transitions in such systems. We investigate the 1d model for TASEP generalized to allow the long-range hopping with the probability decaying with distance $l$ as $1/l^{\sigma+1}$. Monte Carlo studies show that, with properly chosen boundary conditions, the phase diagram for $\sigma>1$ remains the same as in the short-range case, but the density profiles display additional features when $1<\sigma<2$ [2]. At the first-order transition line we observe the phase separation, which can be derived analytically in terms of the domain-wall theory and shares some common features with TASEP in the presence of Langmuir kinetics [3]. In the maximum-current phase the density profile has an algebraic decay with an exponent that depends on $\sigma$ for $1<\sigma<2$ and attains the short-range value $1/2$ for $\sigma\geq 2$. We show that the same scaling exponent and its short-range limit are already present in the numerical solution of the stationary equations for the density profile in the mean-field approximation. Dynamic scaling related to the evolution towards the stationary state was also investigated. We show, in the context of the domain-wall theory, that the dynamical exponent $z$ on the coexistence line is equal to $2$ in the infinite-length limit. We also recover the KPZ exponent $z=3/2$ for the case of the half-filled periodic chain both by Monte Carlo simulations and by showing that the macroscopic density profile in the infinite chain evolves according to the inviscid Burgers equation as in the short-range case.\\ 1) B. Derrida, J.L. Lebowitz, E.R. Speer, Phys. Rev. Lett. 87, 150601 (2001)\\ 2) J. Szavits-Nossan and K. Uzelac, Phys. Rev. E 74, 051104 (2006)\\ 3) R. Juh\'asz and L. Santen, J. Phys. A: Math. Gen. 37, 3933 (2004)}, keywords = {asymmetric equilibrium exclusion hopping long-range out phase process statphys23 topic-3 transitions } } @incollection{statphys23_0587, title = {Generalization of the invaded cluster algorithm to the tricritical point}, address = {Genova, Italy}, author = {I. Balog and K. Uzelac}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=587}, year = {2007}, biburl = {http://www.bibsonomy.org/bibtex/2e55fbcc4778a10716d7c497102e10db0/statphys23}, abstract = {The invaded cluster (IC) algorithm [1] is generalized [2] to the tricritical point on the example of 2D Potts model with annealed dilution. Self-regulating procedure that locates the tricritical point in the two-parameter phase space spanned by temperature and chemical potential of vacancies is constructed based on geometrical arguments. The tricritical point is defined as a simultaneous percolation of the Fortuin-Kasteleyn cluster and the geometrical cluster consisting of vacancies and single spins. The tricritical values of parameters and concentration are presented for q = 1, 2, and 3 and found to be in good agreement with the best known results [3]. Scaling properties of the percolating cluster and related tricritical exponents are also derived. Based on the idea that effective correlation of vacancies is important at the tricritical point, we also examine alternative stopping rules within generalized IC algorithm, and possible extension to higher dimensions.\\ 1) J.Machta, Y.S.Choi, A.Lucke, T.Schweitzer, L.M.Cahyes, Phys. Rev. E 54, 1332 (1996)\\ 2) I.Balog, K.Uzelac, preprint cond-mat/0703759\\ 3) H.Qian, Y.Deng, H.W.J.Bloete, Phys. Rev. E 72, 056132 (2005)}, keywords = {algorithms annealed cluster disorder mc model phenomena potts random statphys23 topic-2 tricritical } }