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• W2269882578 endingPage "184002" @default.
• W2269882578 startingPage "184002" @default.
• W2269882578 abstract "We consider the Forrester-Baxter RSOS lattice models with crossing parameter $lambda=(m'!-!m)pi/m'$ in Regime~III. In the continuum scaling limit, these models are described by the minimal models ${cal M}(m,m')$. We conjecture that, for $lambda<pi/n$, the $ntimes n$ fused RSOS models with $nge 2$ are described by the higher-level coset $(A^{(1)}_1)_kotimes (A^{(1)}_1)_n/(A^{(1)}_1)_{k+n}$ at fractional level $k=nM/(M'!-!M)-2$ with $(M,M')=big(nm-(n!-!1)m',m'big)$. To support this conjecture, we investigate the one-dimensional sums arising from Baxter's off-critical corner transfer matrices. In unitary cases ($m=m'!-!1$) it is known that, up to leading powers of $q$, these coincide with the branching functions $b_{r,s,ell}^{m'!-n,m'!,n}(q)$. For general nonunitary cases ($m<m'!-!1$), we identify the ground state one-dimensional RSOS paths and relate them to the quantum numbers $(r,s,ell)$ in the various sectors. For $n=1,2,3$, we obtain the local energy functions $H(a,b,c)$ in a suitable gauge and verify that the associated one-dimensional sums produce finitized forms that converge, as $N$ becomes large, to the fractional level branching functions $b_{r,s,ell}^{M,M'!,n}(q)$. Extending the work of Schilling, we also conjecture finitized bosonic branching functions $b_{r,s,ell}^{M,M'!,n;(N)}(q)$ for general $n$ and check that these agree with the one-dimensional sums for $n=1,2,3$ out to system sizes $N=14$. Lastly, the finitized Kac characters $chi_{r,s,ell}^{P,P'!,n;(N)}(q)$ of the $ntimes n$ fused logarithmic minimal models ${cal LM}(p,p')$ are obtained by taking the {em logarithmic limit/} $m,m'toinfty$ with $m/m'to p/p'+$." @default.
• W2269882578 created "2016-06-24" @default.
• W2269882578 creator A5057979071 @default.
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• W2269882578 date "2016-03-30" @default.
• W2269882578 modified "2023-09-25" @default.
• W2269882578 title "Fused RSOS lattice models as higher-level nonunitary minimal cosets" @default.
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• W2269882578 doi "https://doi.org/10.1088/1751-8113/49/18/184002" @default.
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