Is it legal to incur debt in your spouse's name?

My husband cheated on me, got the other woman pregnant, and left me. This was after his unemployed ass sat around for over a year letting me support him. (I didn't leave because he was a nice guy to begin with (all an act) and I didn't want to feel like a failure by giving up on the relationship and divorcing him). We are still legally married. While we haven't lived together in a few months, I was wondering if I am legally allowed to create debt in his name. We live in a community property state, and I know his social and all the information necessary to fill out the paperwork. He doesn't know my social (something he let slip when he asked for it for income tax purposes. I refused to provide it), so I don't have to worry about his doing the same thing to me. He is a horrible human who admitted he only married me to get out of the army barracks. He quit a few months after we got an apartment together/saved up a bit of the extra cash to blow on drugs while I was at work.
I'm only stating this to hopefully ease the guilt of people who try to help me. No need to feel guilt, he is horrible. SO... I am having difficulty finding the answer online. Does anybody here know if it is legal to incur debt in your spouse's name if you no longer live together? (We are not divorced or legally separated. He is living off the woman he got pregnant and is her problem now).
Is it legal to incur debt in your spouse's name?
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