we can define a ratio of components | | = g() that again converges as slowly as $\Gamma_{\epsilon}^{0}$.

TCSA for Ising field theory
===========================

We would like now to consider a generic perturbation of the critical Ising model with $m\ne 0 $ and $h\ne 0$. For real-valued $h\ne 0$ the system flows to a trivial theory with a single vacuum. We can study numerically the ratios $\Gamma_{\epsilon,\sigma}^{0}$ using TCSA.

We work in the massless fermion physical space ${\cal H}_{0}$. The perturbed Euclidean action of the Ising field theory is given in (\[IFT\]). Let us choose an orthonormal basis in ${\cal H}_{0}$ described in section \[preliminaries\]. In the NS sector we choose \[basis1\] ||k\_1, …|k\_[p]{}; k\_[1]{}, …k\_[q]{}\_[NS]{} = |a\_[|k\_1]{}\^…|a\_[|k\_p]{}\^a\_[k\_[1]{}]{}\^…a\_[k\_q]{}\^|0 where k\_[i]{}, |k\_[j]{} 1/2 + [Z]{} , k\_i&gt;0 , |k\_j &gt; 0 , p+q - and |k\_1 &gt; |k\_2 &gt;…&gt; |k\_p , k\_[1]{}&gt; k\_[2]{} &gt;…&gt; k\_[q]{} . In the R-sector we choose \[basis2\] ||n\_1, …|n\_[p]{}; n\_[1]{}, …n\_[q]{}\_[R]{} = |a\_[|n\_1]{}\^…|a\^\_[|n\_p]{}a\^\_[n\_[1]{}]{}…a\_[n\_q]{}\^| , p + q - and \[basis3\] ||n\_1, …|n\_[p]{}; n\_[1]{}, …n\_[q]{}\_[R]{} = |a\_[|n\_1]{}\^…|a\^\_[|n\_p]{}a\^\_[n\_[1]{}]{}…a\_[n\_q]{}\^| , p + q - . Here we assume n\_[i]{}, |n\_j , n\_[i]{}&gt;0, |n\_j&gt;0 and |n\_1 &gt; |n\_2 &gt;…&gt; |n\_p , n\_[1]{}&gt; n\_[2]{}&gt; …&gt; n\_[q]{} . We are going to 