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Quantum Critical Matter and Phase Transitions Chapter 280 295 t 1⁄4 T Tc , where Tc is the transition temperature itself, the Tc behaves as a power law, Cv $ jtja, where a is the specific heat critical exponent. A typical example is shown in Fig. 1, which shows the specific heat around the ferromagnetic transition in EuO. Any phase transition can be described by an order parameter, a quantity that is zero in one phase and nonzero in the other. In a ferromagnet, this would be the net magnetization; in an antiferromagnet, the staggered magne- tization; and in a superconductor, the superfluid density. Unlike a first order transition, where the order parameter jumps discontinuously, the order param- eter m at a CPT goes to zero in a power-law fashion, m $ ðtÞb, (2) for t<0, and where b is the order parameter critical exponent. The key element of a CPT is that at the transition, fluctuations at all length scales play an important role. Away from the critical point, fluctuations of the order parameter have a typical finite correlation length x. This correlation 50 40 30 Sample I Sample II x $ jtjn (3) specific heat (1) length diverges close to the critical point, 65 67 69 71 T (K) The specific heat around the ferromagnetic transition in EuO, at Tc 1⁄4 69 K. The critical exponent is a %0.044, indicating a near logarithmic divergence. According to Kornblit, A., Ahlers, G., 1975. Heat capacity of EuO near the Curie temperature. Phys. Rev. B 11 (7), 2678-2688. FIG. 1 CP (J mol–1 K–1)PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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