11 Blume-Capel model. It has been pointed out that the behavior of this system is very interesting and in partic- ular the strong-disorder regime may include many further challenges and open problems that, at the moment, are not fully understood. In our opinion, this is a rather complex subject deserving further research. The authors acknowledge useful e-mail correspondence with X.T. Wu. This research was supported by the Spe- cial Account for Research Grants of the University of Athens under Grant No. 70/4/4071. Acknowledgments FIG. 11: Ground-state behavior of the order parameter of the 2d random-bond BC model versus r for various values of Δ averaged over 250 disorder realizations. GLYPH<s48>GLYPH<s46> GLYPH<s48> GLYPH<s48>GLYPH<s46> GLYPH<s50> GLYPH<s48>GLYPH<s46> GLYPH<s52> GLYPH<s48>GLYPH<s46> GLYPH<s54> GLYPH<s48>GLYPH<s46> GLYPH<s56> GLYPH<s49>GLYPH<s46> GLYPH<s48> GLYPH<s48>GLYPH<s46> GLYPH<s54>GLYPH<s53> GLYPH<s48>GLYPH<s46> GLYPH<s55>GLYPH<s48> GLYPH<s48>GLYPH<s46> GLYPH<s55>GLYPH<s53> GLYPH<s48>GLYPH<s46> GLYPH<s56>GLYPH<s48> GLYPH<s48>GLYPH<s46> GLYPH<s56>GLYPH<s53> GLYPH<s48>GLYPH<s46> GLYPH<s57>GLYPH<s48> GLYPH<s48>GLYPH<s46> GLYPH<s57>GLYPH<s53> GLYPH<s49>GLYPH<s46> GLYPH<s48>GLYPH<s48> GLYPH<s49>GLYPH<s46> GLYPH<s48>GLYPH<s53> GLYPH<s32> GLYPH<s32> GLYPH<s114>GLYPH<s32>GLYPH<s61>GLYPH<s32>GLYPH<s74> GLYPH<s50> GLYPH<s32>GLYPH<s47>GLYPH<s32>GLYPH<s74> GLYPH<s49> GLYPH<s91> GLYPH<s77> GLYPH<s40> GLYPH<s84> GLYPH<s32> GLYPH<s61> GLYPH<s32> GLYPH<s48> GLYPH<s41> GLYPH<s93> GLYPH<s97> GLYPH<s118> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s76>GLYPH<s32>GLYPH<s61>GLYPH<s32>GLYPH<s51> GLYPH<s48> [1] A.B. Harris, J. Phys. C 7 , 1671 (1974). [2] A.N. Berker, Phys. Rev. B 42 , 8640 (1990). [3] M. Aizenman and J. Wehr, Phys. Rev. Lett. 62 , 2503 (1989); 64 , 1311(E) (1990). [4] K. Hui and A.N. Berker, Phys. Rev. Lett. 62 , 2507 (1989); 63 , 2433(E) (1989). [5] A.N. Berker, Physica A 194 , 72 (1993). [6] A. Falicov and A.N. Berker, Phys. Rev. Lett. 76 , 4380 (1996). [7] R.L. Greenblatt, M. Aizenman, and J.L. Lebowitz, Phys. Rev. Lett. 103 , 197201 (2009); Physica A (to appear), also at arXiv:0912.1251. [8] N.G. Fytas, A. Malakis, and I.A. Hadjiagapiou, J. Stat. Mech. (2008) P11009. [9] G. Grinstein and A. Luther, Phys. Rev. B 13 , 1329 (1976). [10] R. Fisch, J. Stat. Phys. 18 , 111 (1978). [11] V.S. Dotsenko and V.S. Dotsenko, Sov. Phys. JETP Lett. 33 , 37 (1981). [12] B.N. Shalaev, Sov. Phys. Solid State 26 , 1811 (1984). [14] A.W.W. Ludwig, Nucl. Phys. B 285 , 97 (1987). [13] R. Shankar, Phys. Rev. Lett. 58 , 2466 (1987). [15] J.-S. Wang, W. Selke, V.S. Dotsenko, and V.B. Andre- ichenko, Physica A 164 , 221 (1990). [16] J.-K. Kim and A. Patrascioiu, Phys. Rev. Lett. 72 , 2785 (1994). [17] V. Dotsenko, M. Picco, and P. Pujol, Nucl. Phys. B 455 , 701 (1995). [18] F.D.A. Aar˜ ao Reis, S.L.A. de Queiroz, and R.R. dos San- tos, Phys. Rev. B 54 , R9616 (1996). [19] H.G. Ballesteros, L.A. Fern´ andez, V. Mart´ın-Mayor, A. Mu˜ noz Sudupe, G. Parisi, and J.J. Ruiz-Lorenzo, J. Phys. A 30 , 8379 (1997). [20] W. Selke, L.N. Shchur, and O.A. Vasilyev, Physica A 259 , 388 (1998). [21] G. Mazzeo and R. K¨ uhn, Phys. Rev. E 60 , 3823 (1999). [22] P.H.L. Martins and J.A. Plascak, Phys. Rev. E 76 , 012102 (2007). [23] M. Hasenbusch, F.P. Toldin, A. Pelissetto, and E. Vicari, Phys. Rev. E 78 , 011110 (2008). [44] D.P. Landau, Phys. Rev. Lett. 28 , 449 (1972); A.N. [43] N.G. Fytas, A. Malakis, and K. Eftaxias, J. Stat. Mech. (2008) P03015. [42] A. Malakis and N.G. Fytas, Phys. Rev. E 73 , 016109 (2006). [41] A. Malakis, S.S. Martinos, I.A. Hadjiagapiou, N.G. Fy- tas, and P. Kalozoumis, Phys. Rev. E 72 , 066120 (2005). [40] A. Malakis, A. Peratzakis, and N.G. Fytas, Phys. Rev. E 70 , 066128 (2004). [39] F. Wang and D.P. Landau, Phys. Rev. E 64 , 056101 (2001). [38] F. Wang and D.P. Landau, Phys. Rev. Lett. 86 , 2050 (2001). [37] A. Malakis, A.N. Berker, I.A. Hadjiagapiou, and N.G. Fytas, Phys. Rev. E 79 , 011125 (2009). [36] V.O. ¨ Oz¸celik and A.N. Berker, Phys. Rev. E 78 , 031104 (2008). [35] O.D. Rodriguez Salmon and J.R. Tapia, arXiv: 0910.3202. [34] I. Puha and H.T. Diep, J. Magn. Magn. Mater. 224 , 85 (2001). [33] M. Kaufman and M. Kanner, Phys. Rev. B 42 , 2378 (1990). [32] H.W. Capel, Physica (Utr.) 32 , 966 (1966); 33 , 295 (1967); 37 , 423 (1967). [31] M. Blume, Phys. Rev. 141 , 517 (1966). [30] M. Picco, Phys. Rev. B 54 , 14930 (1996); Phys. Rev. Lett. 79 , 2998 (1997). [29] J.L. Jacobsen and J. Cardy, Nucl. Phys. B 515 701 (1998). [28] S. Wiseman and E. Domany, Phys. Rev. E 51 , 3074 (1995). [27] S. Chen, A.M. Ferrenberg, and D.P. Landau, Phys. Rev. E 52 , 1377 (1995). [26] A.W.W. Ludwig and J.L. Cardy, Nucl. Phys. B 285 , 687 (1987). [25] J.T. Chayes, L. Chayes, D.S. Fisher, and T. Spencer, Phys. Rev. Lett. 57 , 2999 (1986). [24] A. Gordillo-Guerrero, R. Kenna, and J.J. Ruiz Lorenzo, AIP Conf. Proc. 1198 , 42 (2009).