Boundary criticality of the O(N) model in d = 3 critically revisited
Boundary criticality of the O(N) model in d = 3 critically revisited
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DOI：
10.21468/scipostphys.12.4.131
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发表时间：
2020-09
期刊：
影响因子：
5.5
通讯作者：
M. Metlitski
中科院分区：
文献类型：
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作者：
M. Metlitski
已知d > 3d gt;3维经典O（N）O（N）模型在其体临界点存在三个边界普适类：普通普适类、特殊普适类和特殊普适类.对于普通的过渡，体积和边界顺序同时;特别的不动点对应于在有序边界的存在下发生的体积过渡，而特殊的不动点对应于普通和特别的类之间的边界相变。虽然普通不动点在d = 3d=3中仍然存在，但当d = 3d=3且N \ge 2N≥2时，特殊不动点会发生什么就不太清楚了。在这里，我们表明，正式处理NN作为一个连续的参数，存在一个临界值N_c > 2Ncgt;2分开两个不同的制度。对于2 \leq N 2≤NNc，特殊不动点在d = 3d=3中存在，尽管是以一种修改的形式：长程边界序丢失了，相反，序参数相关函数以\log rlogr的幂衰减。当N > N_cNgt;Nc时，不存在序参量相关衰减慢于幂律的不动点.我们讨论了几种情况下的相图过去N = N_cN=Nc的演变。我们的研究结果似乎是一致的，最近的Monte Carlo研究的经典模型与N = 2N=2和N = 3 N =3。我们还比较了我们的结果在2+1D量子自旋模型的边界临界的数值研究。
It is known that the classical O(N)O(N) model in dimension d > 3dgt;3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. For the ordinary transition the bulk and the boundary order simultaneously; the extra-ordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3d=3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3d=3 and N \ge 2N≥2. Here we show that formally treating NN as a continuous parameter, there exists a critical value N_c > 2Ncgt;2 separating two distinct regimes. For 2 \leq N 2≤NNc the extra-ordinary fixed point survives in d = 3d=3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of \log rlogr. For N > N_cNgt;Nc there is no fixed point with order parameter correlations decaying slower than power law. We discuss several scenarios for the evolution of the phase diagram past N = N_cN=Nc. Our findings appear to be consistent with recent Monte Carlo studies of classical models with N = 2N=2 and N = 3N=3. We also compare our results to numerical studies of boundary criticality in 2+1D quantum spin models.