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In fact, frustration can arise with purely anti-ferromagnetic interactions, for example via different neighbours, and even nearest-neighbour ferromagnetism can be frustrated if there are other constraints, such as the 'spin ice rule'.
-
In fact, frustration can arise with purely anti-ferromagnetic interactions, for example via different neighbours, and even nearest-neighbour ferromagnetism can be frustrated if there are other constraints, such as the 'spin ice rule'.
-
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19
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84907895508
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The reader is referred to the literature, such as cited above (e.g. ()), for further details of the theory of SK-type spin glasses. We do, however, note again that its solution has exposed many new concepts which have had significant consequences in several branches of the science of complex systems (e.g. ) and in mathematics (e.g. ()).
-
The reader is referred to the literature, such as cited above (e.g. ()), for further details of the theory of SK-type spin glasses. We do, however, note again that its solution has exposed many new concepts which have had significant consequences in several branches of the science of complex systems (e.g. ) and in mathematics (e.g. ()).
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For the thermoremanent magnetization (TRM) the system is cooled in the field. For the isothermal remanent magnetization (IRM), the field is applied only after cooling.
-
For the thermoremanent magnetization (TRM) the system is cooled in the field. For the isothermal remanent magnetization (IRM), the field is applied only after cooling.
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Note that strain coupling is required to get the tetragonal crystal structure distortion of the ferromagnetic phase at larger x. However, the present interest is in the relaxor phase which has neither overall polarization nor change in average crystal structure.
-
Note that strain coupling is required to get the tetragonal crystal structure distortion of the ferromagnetic phase at larger x. However, the present interest is in the relaxor phase which has neither overall polarization nor change in average crystal structure.
-
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58
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84907901361
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Note that an antiferromagnetic interaction of longer than nearest neighbour range can already be frustrated. As an example of spin glass behaviour with purely dipolar interaction in combination with site-dilution, see ().
-
Note that an antiferromagnetic interaction of longer than nearest neighbour range can already be frustrated. As an example of spin glass behaviour with purely dipolar interaction in combination with site-dilution, see ().
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As noted earlier, the discussion above has excluded the strain coupling and absorbed the Ba and O ion effects into an effective B- B interaction. To deal with the ferroelectric phase more completely these need to be included.
-
As noted earlier, the discussion above has excluded the strain coupling and absorbed the Ba and O ion effects into an effective B- B interaction. To deal with the ferroelectric phase more completely these need to be included.
-
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-
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61
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in: Stealing the Gold, edited by P. M. Goldbart, N. Goldenfeld, and D. Sherrington (Oxford University Press, Oxford, 2005) -.
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G. Parisi, in: Stealing the Gold, edited by P. M. Goldbart, N. Goldenfeld, and D. Sherrington (Oxford University Press, Oxford, 2005), pp. 192-210.
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Parisi, G.1
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63
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84907901359
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The so-called Burns temperature presumably corresponds to the onset of nanodomains, given by when the density of states of the Anderson-like equation cross zero, while the onset of non-ergodicity and the relaxor transition occurs when the lower Anderson mobility edge crosses zero.
-
The so-called Burns temperature presumably corresponds to the onset of nanodomains, given by when the density of states of the Anderson-like equation cross zero, while the onset of non-ergodicity and the relaxor transition occurs when the lower Anderson mobility edge crosses zero.
-
-
-
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66
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-
84907901358
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-
The ionic radii of Pb++ and Ba++ are, respectively, and 149pm. That of O --is 126pm.
-
The ionic radii of Pb++ and Ba++ are, respectively, 133 and 149pm. That of O --is 126pm.
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, vol.133
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70
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Microstructure of Martensite (Oxford University Press, Oxford, 2003).
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Note that even pure TiNi is often referred to as an alloy, as in 'shape-memory alloy', but in fact it is a compound. When the expression 'alloy' is used in this paper it refers to systems that deviate in a random fashion from a periodic structure.
-
Note that even pure TiNi is often referred to as an alloy, as in 'shape-memory alloy', but in fact it is a compound. When the expression 'alloy' is used in this paper it refers to systems that deviate in a random fashion from a periodic structure.
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Note, however, that actually the V of Eq. (and its extension to higher dimension) decays with an inverse power law p=d just beyond the realm of applicability of the proof of (), together with an extra angular factor. Hence boundary effects are more important in this pure case. But the main interest here is in the disordered alloy extension.
-
Note, however, that actually the V of Eq. (and its extension to higher dimension) decays with an inverse power law p=d just beyond the realm of applicability of the proof of (), together with an extra angular factor. Hence boundary effects are more important in this pure case. But the main interest here is in the disordered alloy extension.
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77
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Note that for x≠1 the twinned phase will have defects.
-
Note that for x≠1 the twinned phase will have defects.
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78
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The SK model, exact for infinite-ranged interactions, has a 'mixed' phase for an x-region above xc, but such a phase in short-ranged spin glasses is contentious. In the martensitic alloys the interactions are power-law, which may suffice.
-
The SK model, exact for infinite-ranged interactions, has a 'mixed' phase for an x-region above xc, but such a phase in short-ranged spin glasses is contentious. In the martensitic alloys the interactions are power-law, which may suffice.
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Note that the phase lines in the strain glass predictions shown in the figures are schematic. In particular, the sign of the slope between the martensitic phase and the mixed phase in the figure for a continuous is not calculated and hence its prediction is currently uncertain.
-
Note that the phase lines in the strain glass predictions shown in the figures are schematic. In particular, the sign of the slope between the martensitic phase and the mixed phase in the figure for a continuous is not calculated and hence its prediction is currently uncertain.
-
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84
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For low fields the GT shift goes as H2 and the AT crossover as H2/3, where H is the applied field.
-
For low fields the GT shift goes as H2 and the AT crossover as H2/3, where H is the applied field.
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This paper does not, however, cite these predictions.
-
This paper does not, however, cite these predictions.
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By 'non-trivial' we refer to a situation where the random fields are essential for the phase transition. Thus, the (soluble) infinite-ranged ferromagnet with random fields is 'trivial' in that the only phases are paramagnet and ferromagnet.
-
By 'non-trivial' we refer to a situation where the random fields are essential for the phase transition. Thus, the (soluble) infinite-ranged ferromagnet with random fields is 'trivial' in that the only phases are paramagnet and ferromagnet.
-
-
-
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102
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84907901347
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-
Note, however, that the spin glass phase is not induced by the random fields, so this system is still 'trivial' in the sense of footnontrivial although the solution of this model requires subtle mathematics.
-
Note, however, that the spin glass phase is not induced by the random fields, so this system is still 'trivial' in the sense of footnontrivial although the solution of this model requires subtle mathematics.
-
-
-
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103
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84907901346
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-
When Ti are displaced in relaxor BZT they do provide extra quasi-random fields but these are secondary to the interaction-driven terms discussed above.
-
When Ti are displaced in relaxor BZT they do provide extra quasi-random fields but these are secondary to the interaction-driven terms discussed above.
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in: Electron-Phonon Interactions and Phase Transitions, edited by T. Riste, Nato Advanced Study Institute Series, Series B: Physics, Vol. 29 (Plenum Press, New York, 1977), p. 209.
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R. B. Stinchcombe, in: Electron-Phonon Interactions and Phase Transitions, edited by T. Riste, Nato Advanced Study Institute Series, Series B: Physics, Vol. 29 (Plenum Press, New York, 1977), p. 209.
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Stinchcombe, R.B.1
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