Abstract
Dilution and randomness are extremely important elements which leads to rich physical phenomena in condensed matter. As one of the simplest systems, diluted and random transverse Ising systems have attracted enormous interests in both theoretical and experimental studies. In general, the quenched dilution gives rise to the percolation phenomena in magnetic systems. In the first part of Chap. 5 focuses on this percolation behaviour in the presence of the quantum fluctuation. On the other hand, the randomness not only modifies the critical property of a quantum phase transition but also gives rise to the Griffiths singularity near a quantum phase transition, even if the randomness does not involves frustration. The latter part of Chap. 5 discusses such unusual properties near a quantum phase transition of random transverse field Ising models.
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Bhattacharya, S., Ray, P.: A diluted quantum transverse Ising model in two dimensions. Phys. Lett. A 101(7), 346–348 (1984). [1.3, 5.2]
Fisher, D.S.: Random transverse field Ising spin chains. Phys. Rev. Lett. 69, 534–537 (1992). [1.3, 5.3, 8.5.2]
Fisher, D.S.: Critical behavior of random transverse-field Ising spin chains. Phys. Rev. B 51, 6411–6461 (1995). [1.3, 5.3, 8.5.2]
Fisher, D.S.: Phase transitions and singularities in random quantum systems. Phys. A, Stat. Mech. Appl. 263(1–4), 222–233 (1999). [1.3, 5.3]
Fisher, D.S., Young, A.P.: Distributions of gaps and end-to-end correlations in random transverse-field Ising spin chains. Phys. Rev. B 58, 9131–9141 (1998). [1.3, 5.3]
Fradkin, E., Susskind, L.: Order and disorder in gauge systems and magnets. Phys. Rev. D 17, 2637–2658 (1978). [5.2]
Griffiths, R.B.: Nonanalytic behavior above the critical point in a random Ising ferromagnet. Phys. Rev. Lett. 23, 17–19 (1969). [5.3]
Harris, A.B.: Effect of random defects on the critical behaviour of Ising models. J. Phys. C, Solid State Phys. 7(9), 1671 (1974). [1.3, 5.2]
Harris, A.B.: Upper bounds for the transition temperatures of generalized Ising models. J. Phys. C, Solid State Phys. 7(17), 3082 (1974). [1.3, 5.2]
Iglói, F., Monthus, C.: Strong disorder RG approach of random systems. Phys. Rep. 412(5–6), 277–431 (2005). [1.3, 5.1, 8.5.2]
Karevski, D., Lin, Y.C., Rieger, H., Kawashima, N., Igli, F.: Random quantum magnets with broad disorder distribution. Eur. Phys. J. B, Condens. Matter Complex Syst. 20, 267–276 (2001). [5.3]
Kovács, I.A., Iglói, F.: Renormalization group study of the two-dimensional random transverse-field Ising model. Phys. Rev. B 82, 054437 (2010). [1.3, 5.3, 8.5.2]
Kovács, I.A., Iglói, F.: Infinite-disorder scaling of random quantum magnets in three and higher dimensions. Phys. Rev. B 83, 174207 (2011). [1.3, 5.3, 8.8]
Landau, D.P., Binder, K.: A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge University Press, Cambridge (2000). [3.2, 5.3, 6.3]
Lin, Y.C., Kawashima, N., Iglói, F., Rieger, H.: Numerical renormalization group study of random transverse Ising models in one and two space dimensions. Prog. Theor. Phys. Suppl. 138, 479–488 (2000). [5.3]
Lubensky, T.C.: In: Balian, R., Maynard, R., Toulouse, G. (eds.) Ill-Condensed Matter. North-Holland, Amsterdam (1979). [5.2]
McCoy, B.: In: Domb, C., Green, M.S. (eds.) Phase Transitions and Critical Phenomena, vol. II. Academic Press, London (1972). [5.2, 5.3]
McCoy, B.M., Wu, T.T.: Theory of a two-dimensional Ising model with random impurities. i. Thermodynamics. Phys. Rev. 176, 631–643 (1968). [5.2, 5.3, 6.4]
McCoy, B.M., Wu, T.T.: Theory of a two-dimensional Ising model with random impurities. ii. Spin correlation functions. Phys. Rev. 188, 982–1013 (1969). [5.2, 6.4]
Motrunich, O., Mau, S.C., Huse, D.A., Fisher, D.S.: Infinite-randomness quantum Ising critical fixed points. Phys. Rev. B 61, 1160–1172 (2000). [5.3]
Pfeuty, P.: The one-dimensional Ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970). [1.1, 1.3, 2.2, 2.2.1, 2.A.3, 4.3, 5.2, 10.1.2]
Pich, C., Young, A.P., Rieger, H., Kawashima, N.: Critical behavior and Griffiths-McCoy singularities in the two-dimensional random quantum Ising ferromagnet. Phys. Rev. Lett. 81, 5916–5919 (1998). [1.3, 5.3]
Rieger, H., Kawashima, N.: Application of a continuous time cluster algorithm to the two-dimensional random quantum Ising ferromagnet. Eur. Phys. J. B, Condens. Matter Complex Syst. 9, 233–236 (1999). [5.3]
Rieger, H., Young, A.P.: Griffiths singularities in the disordered phase of a quantum Ising spin glass. Phys. Rev. B 54, 3328–3335 (1996). [5.3, 6.2, 8.5.2]
Shankar, R., Murthy, G.: Nearest-neighbor frustrated random-bond model in d=2: some exact results. Phys. Rev. B 36, 536–545 (1987). [5.3, 6.4]
Stauffer, D., Aharony, A.: Introduction to Percolation Theory. Taylor & Francis, London (1992). [5.1, 5.2]
Stinchcombe, R.B.: Diluted quantum transverse Ising model. J. Phys. C, Solid State Phys. 14(10), 263 (1981). [1.3, 5.2]
Stinchcombe, R.B.: Exact scalings of pure and dilute quantum transverse Ising chains. J. Phys. C, Solid State Phys. 14(16), 2193 (1981). [1.3, 5.2]
Stinchcombe, R.B.: In: Domb, C., Lebowitz, J.L. (eds.) Phase Transition and Critical Phenomena, vol. VII, p. 151. Academic Press, New York (1983). [1.3, 5.1, 5.2, 6.7.2]
Suzuki, M.: Relationship between d-dimensional quantal spin systems and (d+1)-dimensional Ising systems. Prog. Theor. Phys. 56(5), 1454–1469 (1976). [1.1, 1.3, 3.1, 5.2, 8.7.2, 9.1.2, 9.2, 9.2.4, 9.2.5, 9.2.6]
Tucker, J.W., Saber, M., Ez-Zahraouy, H.: A study of the quenched diluted spin 32 transverse Ising model. J. Magn. Magn. Mater. 139(1–2), 83–94 (1995). [5.2]
Uzelac, K., Jullien, R., Pfeuty, P.: Renormalisation group study of the random Ising model in a transverse field in one dimension. J. Phys. A, Math. Gen. 13(12), 3735 (1980). [5.2]
Vojta, T.: Rare region effects at classical, quantum and nonequilibrium phase transitions. J. Phys. A, Math. Gen. 39(22), 143 (2006). [1.3, 5.1, 8.5.2]
Wu, T.T.: Theory of Toeplitz determinants and the spin correlations of the two-dimensional Ising model. i. Phys. Rev. 149, 380–401 (1966). [5.2]
Young, A.P., Rieger, H.: Numerical study of the random transverse-field Ising spin chain. Phys. Rev. B 53, 8486–8498 (1996). [1.3, 5.3]
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Suzuki, S., Inoue, Ji., Chakrabarti, B.K. (2013). Dilute and Random Transverse Ising Systems. In: Quantum Ising Phases and Transitions in Transverse Ising Models. Lecture Notes in Physics, vol 862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33039-1_5
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