Tricritical behavior

Rossetti GA Jr, Navrotsky A (1999) Calorimetric investigation of tricritical behavior in tetragonal Pb(Zr Tii j )03. J Sol Stat Chem 144 188-194... 

One option to explain classical critical behavior and unusual crossover, is the existence of a tricritical point, which in d 3 is mean-field like [4, 5], In ternary systems, tricritical behavior is generally obtained, if three phases have a common critical point. 

REB Rebelo, L.P. and van Hook, W.A., An imusual phase diagram the polystyrene-acetone system in its hypercritical region near tricritical behavior in a pseudo-binary solution, J. Polym. Sci. PartB Polym. Phys., 31, 895, 1993. 

Along the second-order part of the transition line one would expect 3D-XY critical behavior at least in the limit of the critical point. In real experiments, one observes crossover between XY critical and tricritical behavior, resulting in a ff values where CXxY<0Ceft<0tYc because the temperature range for most experimental data is limited to 10 director fluctuations and the smectic order parameter intervenes as a second source of deviation from isotropic behavior and influences the behavior of the smectic susceptibility and the correlation lengths (parallel and perpendicular to the director) much more than the specific heat. Here also a broad crossover should be ob-... 

Extensive magnetization studies on single crystalspheres with afield applied along a (112) direction in a (111) plane show that the transitions at Hi and H2 are first-order below 4.48 K, and higher than first-order above that temperature up to T, = 4.63 0.02 K. This is tentatively interpreted as tricritical behavior. The high field phase (H>H2) is interpreted as being either... 

It turns out that of = 3 is very special, because it is the upper critical dimension for tricritical behavior. This is the deep reason underlying the fact that polymers at the theta point in = 3 are quasi-ideal (i.e., have size exponent = j and have all dimensionless virial coefficients vanishing in the limit of infinite chain length). In dimension rf < 3, polymers at the theta point are not quasi-ideal." ... 

Unfortunately, a full description of the crossover from tricritical behavior to nonmean-field critical behavior is a difficult theoretical problem [48]. Here, we shall not dwell on recent developments based on the renormalization group approach, since this is outside the scope of the present review, but we only mention the phenomenological extension of the crossover scaling description, Eqs. (24)-(27), to incorporate the Ising behavior [3, 30,49]. There one starts from the observation that the variable appearing in the Ginzburg criterion, r Gi cx is simply proportional to the... 

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