$|+\rangle\!\rangle$, $|-\rangle\!\rangle$ given in (\[conf\_bcs\]). Hence the RG boundary state that corresponds to the $m\to +\infty$ flow is a superposition $$|{\rm RG}\rangle\!\rangle = |+\rangle\!\rangle \oplus |-\rangle\!\rangle \, .$$

For $m<0$ the system is in the high temperature disordered phase. In the R-sector the lowest energy state is the Fock space one-particle excitation $b_{0}^{\dagger}|0\rangle_{\rm R}$ so that all R-sector states disappear from the spectrum as $m\to -\infty$. The remaining vacuum state is |0\_[NS]{}\^[-]{}\_[m-]{} D\_[NS]{}|0\_[NS]{} = \_[n=0]{}\^(-ia\^\_[n+1/2]{}|a\^\_[n+1/2]{})|0 , which as above can be decomposed into the Ishibashi states as |0\_[NS]{}\^[-]{} = |0- | that already corresponds to a normalised Cardy boundary state $|F\rangle\!\rangle = |0\rangle\!\rangle - |\epsilon\rangle\!\rangle $ giving the free boundary condition. Thus in this case |[RG]{}= |F .

In the presence of magnetic field (the case we take up in the next section) the main quantities we will calculate numerically are component ratios of the type (\[gen\_rat\]) discussed in the introduction. Specifically for the massive flows of the Ising field theory it is convenient to introduce two ratios: \[Ising\_ratios\] \_\^[0]{} = , \_\^[0]{} = . Here $|v_{0}\rangle$ stands for the vacuum of perturbed theory as it appears inside the critical Ising state space.

It is instructive to look at these 