%0 Book Section %1 statphys23_0526 %A Anjos, A.S. %A Moreira, D.A. %A Mariz, A.M. %A Nobre, F.D. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K ashkin-teller critical damage-spreading exponents model potts properties simulations statphys23 thermodynamic topic-2 %T Using Exact Relations in Damage-Spreading Simulations: Applications for the Two-Dimensional Potts and Ashkin-Teller Ferromagnets %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=526 %X A powerful computational method for dealing with correlation functions in magnetic systems, based on damage-spreading simulations, is reviewed and tested for two-dimensional ferromagnets. Exact relations involving special kinds of damage and correlation functions, as well as the corresponding order parameters, are used. The efficiency of the method arises through a significant reduction of the finite-size effects, with respect to conventional Monte Carlo simulations. Correlation functions, which represent usually a hard task within this later procedure, appear to be much easily estimated through the present damage-spreading simulations. The method is applied to two well-known ferromagnetic models characterized by nearest-neighbor interactions on a square lattice, namely, the $q$-state Potts and Ashkin-Teller models. In the first model, the effectiveness of the technique is illustrated by an accurate estimate of the exponent $\eta$, of the spin-spin correlation function, for $q=2,3,$ and 4, with rather small lattice sizes, whereas in the cases $q 5$, an analysis of the magnetization is consistent with the well-known first-order phase transition. For the Ashkin-Teller model, we concentrate our analysis along the Baxter line, well known for its continuously varying critical exponents; eight different points along this line are investigated. The efficiency of the method is confirmed through precise estimates of the critical exponents associated with the order parameters (magnetization and polarization), as well as with their corresponding correlation functions, along the Baxter line of the Ashkin-Teller model, in spite of the small lattice sizes considered.

@incollection{statphys23_0526, abstract = {A powerful computational method for dealing with correlation functions in magnetic systems, based on damage-spreading simulations, is reviewed and tested for two-dimensional ferromagnets. Exact relations involving special kinds of damage and correlation functions, as well as the corresponding order parameters, are used. The efficiency of the method arises through a significant reduction of the finite-size effects, with respect to conventional Monte Carlo simulations. Correlation functions, which represent usually a hard task within this later procedure, appear to be much easily estimated through the present damage-spreading simulations. The method is applied to two well-known ferromagnetic models characterized by nearest-neighbor interactions on a square lattice, namely, the $q$-state Potts and Ashkin-Teller models. In the first model, the effectiveness of the technique is illustrated by an accurate estimate of the exponent $\eta$, of the spin-spin correlation function, for $q=2,3,$ and 4, with rather small lattice sizes, whereas in the cases $q \ge 5$, an analysis of the magnetization is consistent with the well-known first-order phase transition. For the Ashkin-Teller model, we concentrate our analysis along the Baxter line, well known for its continuously varying critical exponents; eight different points along this line are investigated. The efficiency of the method is confirmed through precise estimates of the critical exponents associated with the order parameters (magnetization and polarization), as well as with their corresponding correlation functions, along the Baxter line of the Ashkin-Teller model, in spite of the small lattice sizes considered.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Anjos, A.S. and Moreira, D.A. and Mariz, A.M. and Nobre, F.D.}, biburl = {https://www.bibsonomy.org/bibtex/246230e3cf9a927d14576d2e91d5988e0/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {85399774740daf69e4b663ca53f67db9}, intrahash = {46230e3cf9a927d14576d2e91d5988e0}, keywords = {ashkin-teller critical damage-spreading exponents model potts properties simulations statphys23 thermodynamic topic-2}, month = {9-13 July}, timestamp = {2007-06-20T10:16:22.000+0200}, title = {Using Exact Relations in Damage-Spreading Simulations: Applications for the Two-Dimensional Potts and Ashkin-Teller Ferromagnets}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=526}, year = 2007 }