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Let us consider the sentence

We will study certain lattice, or discrete, particle systems.

Let me explain what I am trying to say here. For my potential reader the expressions "lattice particle systems" and "discrete particle systems" are synonymous, and sometimes they have equivalent meanings. In this sentence I aim to establish a convention that those expressions mean exactly the same thing in the following text. (I would like to have two options because I am going to refer to such particle systems multiple times).

Have I chosen a legitimate way to do so?

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Your sentence isn't very clear to me. I suggest something like this:

We will study certain lattice particle systems, herein also referred to as discrete.

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