First, your definition of "deterministic" and "linear classifier" are not clear to me, e.g., is the model building deterministic or model prediction deterministic, In addition, most people will think SVM is not a linear. I am trying to guess what you want to ask from now on.

Most models (not necessary to be "linear") are "deterministic" on prediction stage, and they should be. Intuitively we want this: feeding the same input, we want to have the same output.

However, many models do have some randomness **during the training process** (not the model itself). This means that

- Given the same data, with different random seeds, you can have different models (see [Random Forest](https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm) as an example)
- After model building, it is "deterministic", i.e., feeding same input will have same output.

Finally, in the "linear models" you mentioned logistic regression and SVM, they do not have a random seed during the training process.