Khare Avinash, Christov Ivan C, Saxena Avadh
Raja Ramanna Fellow, Indian Institute of Science Education and Research, Pune 411021, India.
Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Aug;90(2):023208. doi: 10.1103/PhysRevE.90.023208. Epub 2014 Aug 27.
We obtain exact solutions for kinks in ϕ(8), ϕ(10), and ϕ(12) field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically decaying tails and also asymmetric cases with mixed exponential-algebraic tail decay, unlike the lower-order ϕ(4) and ϕ(6) theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the coexistence of up to three distinct kinks (for a ϕ(12) potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the ϕ(10) field theory, which is a quasiexactly solvable model akin to ϕ(6), we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.
我们得到了具有简并极小值的ϕ(8)、ϕ(10)和ϕ(12)场论中扭结的精确解，它们分别可以描述一个二阶相变接着一个一阶相变、两个相继的一阶相变以及一个二阶相变接着两个一阶相变。已知这种相变发生在铁弹性和铁电晶体以及介子物理学中。特别地，我们发现与低阶的ϕ(4)和ϕ(6)场论不同，高阶场论具有代数衰减尾的扭结解以及混合指数 - 代数尾衰减的不对称情形。此外，在我们考虑的所有三个场论中，我们构造了能量相等的不同扭结，并且展示了多达三个不同扭结的共存（对于具有六个简并极小值的ϕ(12)势）。我们还总结了这些系统的声子色散关系，表明高阶场论存在仅允许非线性声子的特定情形。对于类似于ϕ(6)的准精确可解模型ϕ(10)场论，我们还能够在热力学极限下获得经典自由能以及概率分布函数的三个解析解。
