The finite-size scaling relation for the order-parameter probability distribution of the four-dimensional Ising model

Dört boyutlu Ising modelinde düzen parametresi ihtimaliyet dağılımı için sonlu örgü ölçekleme bağıntısı elde edilmektedir. Bu bağıntının geçerli olduğu, Monte Carlo simülasyonları ile sayısal olarak da gösterilmektedir. Kritik noktadaki analitik sonlu örgü ölçekleme fonksiyonunda bulunan sabitler, analitik fonksiyon simülasyonla elde edilen sayısal sonlu örgü ölçekleme fonksiyonuna uydurularak, bulunmaktadır.

Dört boyutlu Ising modelinde düzen parametresi ihtimaliyet dağılımı için sonlu örgü ölçekleme bağıntısı

The finite-size scaling relation for the order-parameter probability distribution of the four-dimensional Ising model is obtained. It is tested and verified numerically by Monte Carlo simulations.The constants of the critical finite-size scaling function in the analytical form are determined by fitting it to the finite-size scaling function obtained numerically. PACS numbers: 05.50.+q, 64.60.Cn, 75.40.Cx, 75.40.Mg

PDF

___

1. Binder, K., 'Finite-size scaling analysis of Ising model block distribution functions', Z. Phys. B, 43: 119-140 (1981).
2. Binder, K., 'Critical properties from Monte Carlo coarse graining and renormalization', Phys. Rev. Lett., 47: 693-696(1981).
3. Bruce, A.D., 'Probability density functions for collective coordinates in Ising-like systems', J. Phys. C, 14: 3667-3688(1981).
4. Binder, K., Nauenberg, M., Privman, V. and Young, A.P., 'Finite-size tests of hypefscaling', Phys. Rev. B,3h 1498-1502(1985).
5. Brezin, E. and Zinn-Justin, J., 'Finite-size effects in phase transitions', Nucl. Phys. B, 257: 867- 893 (1985).
6. Luijten,.E., Binder, K. and Blöte H.W.J., 'Finite-size-scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model', Eur. Phys. J B, 9: 289-297 (1999).
7. Rudnick, J., Guo, H. and Jasnow, D., 'Finite-size scaling and the renormalization group', J. Stat. Phys., 41: 353-373(1985).
8. Binder, K., 'Some recent progress in the phenomenological theory of finite-size scaling and application to Monte Carlo studies of critical phenomena', in Finite-Size Scaling and Numerical Simulation of Statistical Systems, edited by V. Privman, World Scientific, Singapore,173-221 (1990).
9. Jasnow, D., 'Finite-size scaling, hyperscaling and the renormalization group', in Finite-Size Scaling and Numerical Simulation of StatisticalSystems, edited by V. Privman, World Scientific, Singapore, 99-140 (1990).
10.Bruce, A.D., 'Universality in the two-dimensional continous spin model', J. Phys. A, 18: L873- L877 (1985).
11.Nicolaides, D. and Bruce, A.D., 'Universal configurational structure in two-dimensional scalar models', J. Phys. A,21:233-244(1988).
12.Bruce, A.D. and Wilding, N.B., 'Scaling fields and universality of the liquid-gas critical point', Phys. Rev. Lett., 68:193-196 (1992).
13.Parisi, G. and Ruiz-Lorenzo, J.J., 'Scaling above the upper critical dimension in Ising models', Phys. Rev. B, 54:R3698-R3701 (1996).
14.Lai, P.-Y. and Mon, K.K., 'Finite-size scaling of the Ising model in four dimensions', Phys. Rev. B, 41: 9257-9263(1990).
15.Hilfer, R. and Wilding, N.B., 'Are critical finite-size scaling functions calculable from knowledge of an appropriate critical exponent T,J. Phys. A, 28: L281-L286 (1995).
16.Tsypin, M.M. and Blöte, H.W.J., 'Probability distribution of the order parameter for the three-dimensional Ising-model Universality class: A high-precision Monte Carlo study', Phys. Rev. E, 62: 73-76 (2000).
17.Privman, V. and Fisher, M.E., 'Universal critical amplitudes in finite-size scaling', Phys. Rev. B, 30: 322-327(1984).
18.Privman, V., 'Finite-size scaling theory', in Finite-Size Scaling and Numerical Simulation of Statistical Systems,edited by V. Privman, World Scientific, Singapore, 1-98 (1990).
19.Aktekin, N., 'The finite-size scaling functions of the four-dimensional Ising model', J. Stat Phys., 104: 1397-1406(2001).
20.Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E., 'Equation of state calculations by fast computing machines', J. Chem. Phys., 21: 1087-1092 (1953).
21.Gaunt, D.S., Sykes, M.F. and McKenzie, S., 'Susceptibility and fourth-field derivative of the spin 1/2 Ising model for $T>T_c$ and d=4' J. Phys. A, 12: 871-877 (1979).
22.Kenna, R. and Lang, C.B., 'Renormalization group analysis of finite-size scaling in the $Phi^4_4$ model', Nucl. Phys. B, 393:461-479(1993).
23.Aktekin, N., 'Simulation of the four-dimensional Ising model on the Creutz cellular automaton', Physica A, 232:397-407 (1996).
24.Stauffer, D. and Adler, J., 'Logarithmic factors, critical temperature, and zero temperature flipping in the 4D kinetic Ising model', Int. J. Mod. Phys. C, 8: 263-267 (1997)
25.Aktekin, N., Günen, A. and Sağlam, Z., 'A finite-size scaling study of the four-dimensional Ising model on the Creutz cellular automaton', Int. J. Mod. Phys. C, 10: 875-881 (1999).