We define a generalised model for three-stranded DNA consisting of two chains of one type and a third chain of a different type. The DNA strands are modelled by random walks on the three-dimensional cubic lattice with different interactions between two chains of the same type and two chains of different types. This model may be thought of as a classical analogue of the quantum three-body problem. In the quantum situation it is known that three identical quantum particles will form a triplet with an infinite tower of bound states at the point where any pair of particles would have zero binding energy. The phase diagram is mapped out, and the different phase transitions examined using finite-size scaling. We look particularly at the scaling of the DNA model at the equivalent Efimov point for chains up to 10000 steps in length. We find clear evidence of several bound states in the finite-size scaling. We compare these states with the expected Efimov behaviour.
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