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We consider the zero-temperature fixed points controlling the critical behavior of the $d$-dimensional random-field Ising, and more generally $O(N)$, models.
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On the other hand, when studying the critical behavior at finite temperature, the initial condition is cuspless as avalanches are rounded at all nonzero temperatures. In this case one should also include the flow of the renormalized temperature which is associated with the presence of a thermal boundary layer as one approaches the zero-temperature fixed point. Whether or not the system then flows to the cuspless fixed point when d cusp > d > d DR ( N ) d_{\text{cusp}}>d>d_{\text{DR}}(N) is unclear to us (but of limited physical consequence anyhow)
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M. Tissier and G. Tarjus, Phys. Rev. Lett. 107
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M. Baczyk, M. Tissier, G. Tarjus, and Y. Sakamoto, arXiv:1303.2053 (2013)
2013
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