Surface effects on magnetic phase transitions

摘要: The surface scaling theory previously presented by the authors is developed further, and derived heuristically from a cluster model. Monte Carlo calculations are carried out to obtain spatial temperature dependence of magnetization in Ising Heisenberg systems with free surfaces. exponent ${\ensuremath{\beta}}_{1}$ (surface) layer shown agree value (${\ensuremath{\beta}}_{1}\ensuremath{\approx}\frac{2}{3}$) derived. In system, results at low spin-wave calculation Mills Maradudin. models modified exchange ${J}_{s}=J(1+\ensuremath{\Delta})\ensuremath{\ne}J$ on considered, both mean-field means high-temperature-series expansions. critical ${\ensuremath{\Delta}}_{c}$ for ordering found series be 0.6, compared 0.25. For $\ensuremath{\Delta}g{\ensuremath{\Delta}}_{c}$ there region which behaves like bulk two-dimensional model near its phase transition. exponents experience crossover $\ensuremath{\Delta}={\ensuremath{\Delta}}_{c}$, reflected poorly behaved series, effective differing true ones $\ensuremath{\Delta}\ensuremath{\lesssim}{\ensuremath{\Delta}}_{c}$. case weakened ($0l{J}_{s}lJ$), fit linear over large range below ${T}_{c}$, thus providing possible explanation previous experiments. sufficiently strong negative ${J}_{s}$, predicts that will order antiferromagnetically while ferromagnetic.